^ Sfi/ 



fMKHANICALv 
'-J. DRAWING^- 




Class / 55^ 



Book 
Gopiglit)J° 

COPYRIGHT DEPOSm 



m^ 



••LEARN TO DO A THING BY DOING IT."-old provbrb 

3ELF-HELP 

MECHANICAL DRANx/lNO 

AN EDUCATIONAL TREATISE 




BY 



N. HAWKINS, M, E. 

Author of Handbook of Calculations, etc. 

New York: THEO. AUDEL & CO., 



Publishers 



T353 
.H33 



COPYRIGHTED BY 

THEO. AUDEL 6c CO. 

NEW YORK 

' 1902-1914 



NOV 30 1914 

©CU 38776 'i 



This work 
is 
most kindly and 
respeetfnlly dedicated to 
THE COMING MAN 
who at the present time 
is undoubtedly devot- 
ing a goodly share of 
bis spare time to 
the atndy of 
drawing. 



Preface. 



It is because of a personal and practical experience of the advantage to be gained by the 
possession of a knowledge of drawing, that the author is prompted to undertake the rather pleasant 
task of producing a self-help book relating to the subject. 

Since the days of youthful endeavor, the author has passed through an extended experience 
of mechanical life, and scarcely ever without chalk, pencil or instrument in hand, to illustrate by 
sketch or drawing, the tools to be employed, or to picture the finished product ,■ accordingly, 
thro2ighout this work, words of explanation and the drawings will go together to aid the diligent 
student. 

It has been said by an eminent writer, that "one workman is superior to a^iother — other 
circumstances being the same — directly in proportion to his knowledge in drawing, and those who 
are ignorant of it must in many respects be subservient to others who have obtained that knowledge." 

It has been also said that no man is fitted to be foreman of a shop who cannot draw., and 
it is generally true that no one will be appointed to that position., except temporarily, who does 
not possess some knowledge of the art, either '■'freehand" or instrumental. 

13 



14 Hawkins' Mechanical Drawing. 

It is a question how far a good working knowledge of drawing can be attained without a 
teacher ; it is true that but few have become proficient without such aid, but it is equally true 
that ^^ self-help" has been the key note to all advancement. 

The author received personal instruction in several ways and times, at home, in school, in 
an architect's office, and under an experienced mechanical engineer, but it was in the early morning 
hours of a bright summer time — lang syne — that he made his first serious attempt to master the 
art of mechanical drawing. It was a struggle and a battle to hold himself down to "the board" 
to the finish, but it was a victory — one, won over slothfulness and impatience, and of suck a 
nature as to warrant the use of the term " self help ' to the encouragement of others. 

In conclusion two sentiments m.ay be added; if a good working knowledge of drawing is 
"worth the while," then, I, the student should be thoroughly in earnest in acquiring it; 2, he 
should be willing to take sufficient time and give much hard study to gain the skill necessary for 
success. 

This persistence is not irksome. It carries its own reward, and the results are definite 

and sure. 

" One step and then another, and the longest walk is ended ; 

One stitch and then another, and the largest rent is mended. 
One brick upon another, and the highest wall is made ; 
One flake upon another, and the deepest snow is laid. " 









INTRODUCTION 


El 







Introduction. 



Drawing is one of the arts ; art relates to something to be done, and art in the industrial and mechanical 
sense aims chiefly at utility, and is governed by exact rules; hence mechanical drawing — so-called — tends first to 
be useful and helpful, and second to accuracy in execution, including most minute details; it aspires to the 
perfection of nature in adaptability of the means to the end. 

Drawing constitutes a universal language, to acquire which is a matter of importance, for by its use one is 
able to illustrate the form and dimensions of an object, device, or utility, in very much less time, and far more 
clearly, than by a verbal description. 

To a person who may not be able perfectly to understand the language of a country, to be able to draw is 
an aid and a safeguard ; to use the words of Sir Joshua Reynolds, " the pencil speaks the language of every land." 

In extensive iron works and metal-working establishments the designer and draughtsman is always in 
demand. His services are indispensable and his position is a highly responsible one. It becomes his special 



Hawkins' Mechanical Drawing. 

province to design improvements, to furnish sketches and to make finished drawings; to calculate strains, strength, 
power, motion, weight, friction and durability. All this and much more is the professional draughtsman's work. 

In " directory" classification, he who accomplishes such comprehensive results as above described is termed 
a " Draughtsman , " but the word has as wide a meaning as " Engineer," which takes in civil, mechanical, naval, 
sanitary, steam and other engineering specialists. So, in drafting, it includes the office boy employed in making 
blue prints, it embraces the copyists, tracers and assistants, as well as the head draughtsman and chief engineer. 

Consequently the range is wide, and the line hard to draw between draughtsmen who work with their 
hands, and those who work with their brains. It may be added that the best men are too frequently undervalued, 
owing to the unavoidable difficulty in distinguishing the difference in true worth, between the two widely separated 
classes. 

It may be remarked that they only draw well who draw intelligently ; aptness in this, as in many other 
virtues, is a matter of slow growth, "here a line and there a line" — it's the proper direction, not the rate of 
progress, that counts in the end. 

There are several methods of drawing — I, Free-hand; 2, Instrumental ; 3, Geometrical; 4 Perspective. 
In the first the work, also termed sketching, is executed by pencil, pen, crayon, or even paint-brush; in the second 
the result is attained by the use of rule, tee-square, drawing pen, etc. ; this method is also denominated 
mechanical drawing, and suggests the title of this volume. 

The great usefulness, not to say necessity, of readiness in executing accurately, drawings " to scale," is 



Hawkins' Mechanical Drawing. 

emphasized by the fact that now, more than ever, is all machinery designed, and it may almost be said, is ' built," 
in the draughting room — this is a valuable hint relating to " reading " drawings. 

It is wise, as well as easy, to begin at the beginning of things ; thus, it is altogether the good part to mount 
a ladder by the first and second rounds rather than to attempt it by taking the third, sixth, ninth, etc. — 
especially are first and second rounds the very best to start upon ; " Chalk-work," is the first subject introduced, 
next, that of " Free-hand." These are the first steps leading upward in this most agreeable attainment — skill 
in illustrating and designing of objects, tools, and utilities. 

A single word of advice before introducing the elementary work connected with mechanical drawing : if 
the student should experience difficulty in mastering the diagrams and curves abounding in this book, let him 
consult an experienced draughtsman or teacher, who, by a few strokes of a lead pencil, can easily make them plain ; 
that knowledge — which cannot be printed or self-taught — termed t/ie Craftstnayi s Art, is communicated largely by 
personal telling and showing, from man to man ; in drawing, this help should be thankfully availed of, when 
necessity arises. 

Note — Sketching is often in demand because there is no time for finished or carefnl drawings, and the one who can draw a few 
lines in a moment to let a sadden necessity be known, is the man of the hour. All candidates for First Class Engineer's Certificates in 
marine service in the navy have to undergo an examination in rough drawing ; this is intended not so much as a proof cf the applicant 
possessing the capability of a draughtsman, but in the event of any injury to the engines in his charge, so that he may be able to send to 
his Superintendent a rough drawing of the particular part, properly dimensioned, so that it could be worked from, and time saved on the 
arrival of the ship at the port where the repairs are to be done. 



"No matter how thorough our education may have been 
at the first, rules and formulas will slip from, the 
memory, and every days experience gives additional 
evidence of the truth of the old adage that 'the 

KEY THAT RESTS, RUSTS.' "—Simpson Bai,i.ard. 



The plan of the ^O^^K 



The purpose or scope of this work may be briefly stated : It is to aid the aspiring student in making the first 
advance towards a thorough and useful knowledge of drawing in its several divisions, as elsewhere defined. 

The method to be followed in presenting the subject will be the natural order clearly and simply defined, 
as " from the less to the greater." 

The first subject to be discussed comes under the heading of chalk-work, /, e., such drawings as can be 
executed on a blackboard, a floor, or even on more primitive surfaces, such as a smooth stone or board. 

This is indeed a lowly beginning, but the author is quite confident it will awaken as much interest as any part 
of the book — even in the most experienced in the art of drawing, as to them it will revive the ambitions and first 
crude attempts made in the golden days of their youth. 

Let it be clearly understood by all, and especially by those who wish to learn drawing, that the study of this 
delightful art does not require any special qualification. We need only ask one question : Have you learned to 
write? If so, be assured you may learn to draw, but to all the same rule applies, first the elements of the art, and 
afterwards the more advanced study. 

It is not expected that all should exhibit a decided taste for drawing, for the possession of this is rather a gift 
of nature than the result of education ; but a knowledge of principles and a certain amount of executive ability 

21 



iz Hawkins^ Mechanical Drawing, 

may be obtained by every one of average capacity, and whatever the natural power may be, it will be increased 
and developed by exercise ; if the progress is steady and continuous and in the right direction, success is sure to 
crown the work. 

The second division of the book will be free-hand drawing, t. e., that which is executed without instruments. 
Nothing to instruct has been spared in this important step in the path of advancement. 

The illustrations accompanying the two opening sections have been made designedly elementary, for there 
are many who have a taste for drawing and who have a desire to learn, who from place of residence or other 
circumstances have not the opportunity of receiving the assistance of a master. To such this book presents itself 
as a friend directing to the right road, talking, reasoning, and explaining by the way. 

The " chalk-work " and " free-hand " sections of the book relate to the foundations upon which all must rest 
who seek the aid to be derived from the art ; hence, the following pages are written with a view to encourage all, 
and those who are prepared to follow the directions given in them may look forward to the possession of sufficient 
drawing power to add to their usefulness in after life. 

At this point of attainment there arises a need to know the meaning of many words and phrases used by 
draughtsmen ; these are grouped alphabetically from A to Z under the heading of, 

Useful Terms and Definitions : Memorizing these few pages will be of benefit, as an intimate knowledge 
of the language of the drawing office stamps a man as worthy of a hearing, and assures attention to anything 
which he may write or say pertaining to the art. 



Hawkins* Mechanical Drawing. 23 

After the Definitions the subject explained will be the Instruments and Materials used in mechanical 
drawings ; following in due course appear Geometrical and Mechanical Drawing, Gearing, Linear Perspective, Pro- 
jection, Shading, Tracing, Lettering, Drawing OfKce Rules, Reading Drawings, Useful Tables and a General Index, 
to which the student is referred. A careful reading is requested to the following helpful note. 

Grateful acknowledgment is made to George Perrott, Esq., M. E., for practical and technical assistance 
throughout the work, and to Theo. Lucas, Engineer, for text and illustrations in the portions of the book relating 
to Linear Perspective and Projection. 

Note. — In Machinery Prof. Chas. H. Benjamin says, referring to drawing, under heading "How and what to study," ". . . I have 
so far said nothing about drawing, for I do not think it of much use to learn that, until you know what you want of it. All this time that 
you have been studying mechanism you should have had a sketch book or pad of noie paper, and made free hand sketches of mechanical 
movements which interested you and of various machine details. You should accustom yourself to use drawing as a means of expressing 
ideas, just as you use written words, so that it becomes a second nature to you to sketch anything you ^vish to remember or describe. If 
you work from blue-prints in the shop, or if you can borrow some to study, this will help you to understand how a drawing is made. You 
can get some drawing instruments at any time and begin to practice on drawing straight lines and circles, so as to become familiar with 
the instruments. And here it will be of great benefit to you if you can attend an evening drawing school for one night in the week 
at least. 

" When you have become sufficiently familiar with the principles of drawing, a book on mechanism will tell you how to draw gear 
teeth and cams, and how to design various link motions. Make up your own problems from what you see in the shop and make your drawing 
a means to an end and not the principal thing ; it is of little use to be able to make a nice drawing unless you know what to draw and why. 

•''Drawing is a convenient tool as an aid in expressing to others the ideas which you wish to convey ; in all cases take the problems 
and the ideas from your every-day work and that which is around you ; your success will depend upon the close connection which you 
keep at all times between your acquired knowledge and your practical work." 



general Cist of Contents. 



Introduction, .... 1-24 

Chalk Work, .... 25-38 

Preliminary Terms and Definitions, . 39-52 

Freehand Drawing, . . . 53-78 

Geometrical Drawing, . . . 79-100 

Drawing Materials and Instruments, 101-134 

Mechanical Drawing, . . 135-188 

Penciling, ..... 139-147 

Projection, .... 148-164 

Inking in Drawings, . . . 167-170 

Lettering Drawings, . . . 171-175 

Dimensioning Drawings, . . . 176-179 

Shading Drawings, . . . 1 80-1 81 



Section Lining and Colors, . 182-185 

Reproducing Drawings, . . . 186-188 

Drawing Office Rules, . . 189-195 

Gearing, ..... 197-208 

Designing Gears, . . . 209-216 

Working Drawings . . . 219-227 

Reading Working Drawings, . 228-230 

Patent Office Rules for Drawings, . 231-236 

Useful Hints and " Points," . 237-244 

Linear Perspective, . . . 245-265 

Personal, by the Editor, . . 281 

Useful Tables, .... 269-280 

Reference Index, . . . 283 



1 The peculiantv of all art is that it cannot 
be communicated in writing alone, craft is a 


ri 


term which is synonymous with art; a craft 




1 requires manual dexterity which cannot be 




taught in books. 





Gball^ V^opI^. 



The blackboard has been well called the great 
weapon of the modem educator ; this is especially true 
in reference to instruction in an art dealing with lines, 
curves and figures. 

Many a man can chalk out on a blackboard, or on 
a piece of sheet-iron, or on the floor, just what he wants 
to show, and make his meaning very plain ; hence, in 
every workshop, and many other places, a blackboard 




is more than useful, and it has been said that no 
draughting office is complete without one. 
Fig. 6 represents a chalk-crayon. 




Fig- 7. 



28 



Hawkins' Mechanical Drawing. 




Fig. 8. 



Figs. 7 and 8 need no explanation, as they rep- 
resent two forms of the well-known blackboard. 

Chalk lines have this advantage — they are easily 
altered or rubbed out when not needed any longer. 
The work executed upon a blackboard is mostly 
done by hand, without aid from instruments; a few 
tools, however, are useful — such as, i, large Wooden 
blackboard compasses holding a crayon, which are made 
and sold by the trade in size twelve inches to thirty 
inches in length ; 2, a straight-edge ; and 3, some cray- 
ons. With the compasses cirtles and part of the circle 
can be made, and with the straight-edge the larger 
lines can be drawn. •, 

J"hese instruments are shown on page 29, and are, 
I, compasses, for holding chalk for making circles; 2, a 
tee-square ; 3, a straight-edge ; 4, a protractor for meas- 
uring angles ; 5, ^- triangle 60° and 30°; 6j a brass 
holder for crayoHsi I"" ^J*=''' . ^ y:;;:!??:::.; ; . 

Blackboard Dfifvv^ig.-— The Use bf a blackboard 
comes principally and properly under the head of 



i 



Hawkins' Mechanical Drawing 



29 




iiiiiininnifflnimDaiiinnminniriininnnianjmra 



mil mil 



mmminmniiDranniiiMin^^raDDDmmf^rafflra 




30 



Hawkins' Mechanical Drawing. 



free-hand drawing, but its importance is such that a 
separate division of the volume is assigned to it. 

Thus, chalk-work may be considered the first lesson 
in " free-hand,'' as all the examples can also be most 
profitably practiced with pencil and paper. 

Very rapid drawing upon the board should not be 
encouraged, as it is likely not to be accurate enough ; 
again, the board should be entirely free from grease. 
Cloths, sponges or chamois skin rubbers may be used 
to erase or change the chalk marks. Vertical lines 
should be drawn from above downward ; short lines 
should be drawn with the fingers alone, those somewhat 
longer with the hand, using the wrist-joint ; the still 
longer lines with the forearm, using the elbow-joint ; 
those longer yet with the whole arm, using the 
shoulder-joint ; lines should always be drawn with a 
uniform motion, slow enough for the eye to follow. 

Practice in chalk-work should alternate with 
sketching in a sketchbook and with geometrical draw- 
ing — to be hereafter described. The student should 



practice a short time on the board, at least once a week ; 
large sizes are the most profitable for the representations 
to be made ; when drawing in different directions the 
hand should be turned, not the paper or board ; the 
hand should never be allowed to obstruct the sight, 
hence the hand and fingers should be held in a position 
of freedom — with fingers not nearer than l^ or 2 
inches from the board. 

PREPARATORY PRACTICE IN DRAWING. 

Every visible object is bounded by lines which 
enable the observer to determine its shape. If these 

Note. — The first lesson of any kind the author received in 
drawing was to make a straight line ; this was effected by holding 
the pencil nearly erect and guiding it along by the aid of the little 
finger held pressed against the edge of a board ; this was a useful 
item of knowledge, as proved by passing years. 

A well-known artist, in telling his early experience, said : 
" The first thing I was taught was to draw a line, divide it, erect 
a perpendicular from its center, and afterwards to divide the angle 
made by the perpendicular." In answer to a question asking how 
long he was kept at the lines, he replied, " about two months — or 
a month or two," indicating that even the longer time would have 
been well spent in learning to draw a straight line. 



Hawkins' Mechanical Drawing. 



31 



lines are straight or curved, the shape of the object is 
regular ; if broken, the shape of the object is irregular. 
The elements, then, of form are lines, straight, 
curved, or broken, and these, therefore, furnish the 
beginning of all instruction in free-hand or mechanical 
drawing. 

PERPENDICULAR LINES. 

Fig. 1 5 shows six lines — upright and perpendicular, 
with points or " dots " indicated at the top and bot- 
tom of each line ; to draw these, proceed thus : 

I 



■ -■ ■ ■ ■ 

» ■'■ ■ 

* - - ■■■ ■ 



Fig. 15- 



Fig. 16. 



The learner should stand with his right shoulder 
opposite the board, and the w-eight of the hand and the 
arm should be allowed to fall naturally ; now, make on 
the board two points, one being six inches above the 
other, these being merely " dots," shown at the ends of 
the lines, figs. 15, etc., and made with two motions; 
the line between the points should now be drawn 
not too quickly from the upper to the lower point; 
three movements of the hand and arm complete the 
line ; to draw the other five lines the movements have 
simply to be repeated. 

If the student pronounces to himself "one," 
" two," " three," at each motion, it will be helpful ; ia 
this exercise, fig. 15, the aim is to make six lines, each 
line being parallel to the first. Again, in the example, 
it is intended that the lower point should be made 
first, next the upper, and lastly the line drawn from the 
upper to the lower point, but the order may be re- 
versed ; at one the upper point, at two the lower, at 
tAree the stroke upwards to complete the line. 



32 



Hawkins* Mechanical Drawing. 



HORIZONTAL LINES. 

To make these as shown in fig. i6, proceed as 
follows : With the word one make a point, with two 
another point six inches at the left, with tkree draw a 
straight line from the left point to the right. All added 
lines should be parallel : for practice, reverse the process 
thus, one, make a "point," at iwo another point at the 
right, at t/tree draw line to the left. 




Fig. 17. 

The student will note that the two motions — at 
the words one and iwo — are to fix the positions of the 



ends of the lines ; this practice will be found useful in 
the most advanced examples and an item of elementary 
practice never to be forgotten — like the help to be 
derived by the first round of a ladder. 




Fig. i8. 

OBLIQUE LINES. 

_In drawing oblique_ straight lines as shown in fig. 

17^ at the word one let the student make the lower 
point ; at the word iwo the upper, a little to the 



Hawkins' Mechanical Drawing. 



33 



right of the lower; at the word three draw a line 
quickly from the upper to the lower point. In pro- 
nouncing the words one, two, three, let the student 
make the additional parallel lines. 

As shown in fig. i8, at the word one make the lower 
point ; at the word two the upper point, a little to the 
left ; at the word three draw a line rapidly from the 
upper to the lower point, and "timing'' the process 
by repeating one, two, three, piake the additional parallel 
lines. . / 




BROKEN LINES. -, __'^ , " 

A broken lineis^xiom-pbsed of tw(5'T>r more straight 
lines at angles foeaefe-tyther (see fig. 19). To draw 
them begin (saying) (?«^, make a point; two a point 




Fig. 20. 




Fig. 21. 



34 



Hawkins' Mechanical Drawing, 




Fig. 22. 




Fig. 24. 





Fig. 23. 



Fig. 25- 



Hawkins' Mechanical Drawing. 



35 



below at the left ; ikree, a point above at the left ; 
/our, draw a line from the left hand point to the lower 
point ; at the word /ve, from the lower point to the 
upper right hand point. For practice draw numerous 
lines in the same way, keeping them parallel to each 
other, as shown in fig. 20. 

In example, fig. 21, the arrangement of the points 
is changed — let the student draw at the words, as 
follows : One, a point ; two, a point above at the left ; 
three, a point below at the left ; four, draw from the 
point at the left to the upper point; five, from the 
upper point to the lower right hand point ; continue 
to add parallel lines to complete the figure as shown. 

Figs. 22 and 23 are given as examples to practice, 
making first the points and then the connecting 
lines and afterward the parallel lines to complete the 
figures. 

CURVED LINES. 

To draw curved lines, as shown in fig. 24. At the 
word one, point ; at the word two, point three inches 



directly above ; three, at the same distance above again 
make a point ; now draw a curve as shown, joining the 
middle point and the upper point ; now draw the 
curve as shown below it ; finally complete figure 
as shown. 





Fig. 26. 



Fig. 27. 





Fig. 28. 



36 



Hawkins' Mechanical Drawing, 





Fig. 29. 



Fig- 30- 



Figs. 25 to 30 are to be practiced, making first the 
points and then connecting them by the curves to 
complete the figures. 

When two or more students are working together, 
with each having a blackboard, the counting may be 
in concert — or a teacher could count for a class. In 
these linfe examples care should be used in making 

them of uniform length. There is a difference to be 

,' 1' '' I'i •' ' 

noted between a crooked line and a brbken line, the 

latter beiiiga straight line and the fofn^er deviating 
from it. " 



Square chalk crayons are the best for hand work, 
as lines of an even or uniform width can be drawn with 
them, 

A very fine effect is produced by using two thick- 
nesses of chalk, one being double the thickness of the 
other ; the heavy lines being used on the shade side of 
objects will produce a good effect, giving thickness and 
body to the object. 

Round chalk crayons are used in the compasses to 
draw circles, but hand lines drawn with them are not so 
neat as those produced with the square-shaped chalk. 

To obliterate or remove the construction, or false 
lines made on the blackboard, a wooden handle two 
inches in diameter with a cone end 3 or 4 inches long, 
covered with chamois skin or soft cloth tightly wrapped 
round the cone and fastened with a tack or drawing 
pin, makes the best implement to erase lines not 
required , the point of the cone will remove these with- 
out destroying the lines or curves which meet them.- 



Hawkins' Mechanical Drawing. 



37 



Sponges, chamois skin or cloth rubbers are used 
to rub out the chalk drawings and clean the black- 
board. 

The best height for a diagram on the blackboard 
is not higher than the head, nor lower than the elbow. 



Horizontal lines should be made from the left to 
the right ; the body and arm being moved with the 
hand, and kept in the same relative position with it, 
will steady the hand. 



Curved lines to the left should be drawn first, 
enabling the eye to take in not only the curve in pro- 
cess of formation but that already made. 

Passing the crayon in the hand, over the intended 
curve previous to marking it, will guide the eye and 
give confidence to the hand in chalking the curve. 

A proper distance from the blackboard is essential, 
the face being about two feet away from it. 

Draw with the whole arm extended from the 
shoulder-joint, not from the elbow or wrist. 




Fig- 31- 



38 



Hawkins' Mechanical Drawing. 



"There are more ways than one of telliRg 
things; by speech, by writing, hy printing, 
also by pictures and drawings." Knowles, 



I^S 








TERMS DEFINITIONS 




i^^9 




^^P 



40 



Hawkins' Mechanical Drawing, 




:5I,BCTRA, 



preliminapjf ^erms and {definitions. 



Like all the arts, drawing has a nomenclature of its 
own, and nothing can be more helpful to the beginner 
than to know the name of things relating to the art 
of drawing. This is a language almost peculiar to 
itself, and used daily and hourly by many thousands 
of superintendents, foremen and master mechanics, as 
well as by owners, designers and draughtsmen, hence 
its introduction at this early stage. 
ALTITUDE. — This is the elevation of an object above 

its base, or the perpendicular distance between 

the top and bottom of a figure. 
ANGLE is the difference in the direction of two lines 

which meet or tend to meet. The lines are called 

the sides and the point of meeting, the vertex of 

the lines. 



ANGLE. 



To make an angle apparent, 

the two lines must meet in a 

point, as A B zvidi A C, which 

meet in the point A, as shown 

in fig. 33- 




i^-sa- 



Angles are measured by degrees. 

A Degree is one of the three hundred and 
sixty equal parts of the space about a point in a 
plane. 

Angles are distinguished in respect to magni- 
tude by the terms Right, Acute and Obtuse 
Angles. 



42 



Hawkins' Mechanical Drawing. 



ANGLE. 




A Right Angle is that formed 
by one line meeting another, so as 
to make equal angles with that 
other. Pig 3^ 

The lines. forming a right angle zxt. perpendicu- 
lar to each otJier. 

An Acute Angle is less than 
a right angle. See fig. 35. 

An Obtuse Angle is greater 
than a right angle. See fig. 36, 




Fig- 35- 



Obtuse and acute angles are also called oblique 
angles; and lines which 
are neither parallel nor 
perpendicular to each other 
are called oblique lines. ^^S- 36. 

The Vertex or Apex of an angle is the point 
in which the including lines meet. 




ANGLE. 

An angle is commonly designated by a letter 

at its vertex ; but when two or more angles have 

their vertices at the same point, they cannot be 

thus distinguished. 
For example, 

when the three lines 

A B,A C.and A Dm 

fig. 37 meet in the 

common point A, we 

designate either of the 

angles formed, by 

three letters, placing 

that at the vertex Fig. 37« 

between those at the opposite extremities of the 

including lines. Thus, we say, the angle B A C, etc. 
APEX. — The summit or highest point of an object. 
ARC — See circle. 

AXIS OF A SOLID — An imaginary straight line pass- 
ing through its center. 




Hawkins' Mechanical Drawing. 



43 



AXIS OF A FIGURE.— A straight line passing through 
the center of a figure, and dividing it into two 
equal parts. 

BASE. — The base of a solid figure is that on which it 
stands — the lowest part. 

BISECT. — To divide into two equal parts. 

BISECTOR.— A line which bisects. 

CIRCLE.— A Ctrc/e is a plane 
figure bounded by one uni- 
formly curved line, all of the 
points in which are at the 
same distance from a certain 
point within, called the 
Center. Fig. 38. 

The Circumference of a circle is the curved 
line that bounds it. 

The Dia7neter of a circle is a line passing 
through its center and terminating at both ends 
in the circumference, as ^ C B. 




CIRCLE. 

The Radius of a circle is a line extending 
from its center to any point in the circumference. 
It is one half of the diameter. All the diameters 
of a circle are equal, as are also all the radii C D, 
CB and C A. 

An Arc of a circle is any portion of the cir~ 
cumference, as B D and A D. 

Semi-Circle. — Half a circle formed by bisect- 
ing it with a diameter, as A C B. Fig. 38. 

An angle having its vertex at the center of a 
circle is measured by the arc intercepted by its 
sides. Thus, the arc A D measures the angle 
A CD, and in general, to compare different angles, 
we have but to compare the arcs, included by their 
sides, of the equal circles having their centers at 
the vertices of the angles. 

CIRCUMSCRIBE — To draw a line of figures about or 
outside, such as a circle drawn around a square 
touching its corners or angles. 



44 



Hawkins' Mechanical Drawing. 



CIRCUMSCRIBE. 

Inscribe. — To draw a line or figure inside or 
on the interior, such as a circle drawn within a 
square touching its sides. 

CONCAVE. — Curving inwardly. 

CONE. — A solid body or figure having a circle for its 
base, and its top terminated in a point or vertex. 

CONSTRUCTION.— The making of any object. 

CONTOUR.— The outline of the general appearance of 

an object. 
CONVERGENCE. — Lines extending towards a common 

point. 
CONVEX. — Rising or swelling into a round form — the 

opposite to concave. 
CORNER. — The point of meeting of the edges of a 

solid, or the two sides of a plane figure. 
CROSS-HATCHES. — In free-hand drawing the use of 

lines crossing each other to produce light and 

shade effects. 



CURVE. — A line of which no part is straight. 

Reversed Curve. — One whose curvature is first 
in one direction and then in the opposite direction. 

Spiral Curve. — A plain curve which winds 
about and recedes, according to some law, from its 
point of beginning, which is called its center. 

CYLINDER. — A solid bounded by a curved surface and 
by two opposite faces called bases ; the bases may 
be any curved figures and give the name to the 
cylinder; thus a circular cylinder is one whose 
bases are circles. 

CYLINDRICAL Having the general form of a cylinder. 

DEGREE.- The 360th part of a circle. 

DESCRIBE. — To make or draw a curved line ; to draw 
a plan. 

DESIGN. — Any arrangement or combination to pro- 
duce desired results in industry or art. To 
delineate a form or figure by drawing the outline — 
a sketch. 



Hawkins' Mechanical Drawing. 



45 



DEVELOP To unroll or lay out. 

DIAGONAL. — A right line drawn from angle to angle 
of a quadrilateral or many angled figure and 
dividing it into two parts. 

DIAMETER. — A right line passing through the center 
of a circle or other round figure terminated by the 
curve and dividing the figure symmetrically into 
two equal parts. 

EDQE. — The intersection of any two surfaces. . 

ELEVATION. — The term elevation, vertical projection 
and front view — applied to drawings — all have the 
same meaning. 

FACE. — One of the plane surfaces of a solid ; it may 
be bounded by straight or curved edges. 

FINISHING Completing a drawing whose lines have 

been determined by erasing unnecessary lines and 
strengthening and accentuating where this is 
needed. 



FORESHORTENING — Apparent decrease in length, 
owing to objects being viewed obliquely ; thus i 
wheel, when seen obliquely, instead of appearing 
round, presents the apj>earance of an ellipse. 

FREE-HAND — Executed by the hand unaided by 
instruments. 

GENERATED.— Produced by. 

GEOMETRIC. — According to geometry. 

HALF-TINT. — The shading produced by means of 
parallel equidistant lines. 

HEMISPHERE — Half a sphere obtained by bisecting 
a sphere by a plane. 

HORIZONTAL.— Parallel to the surface of smooth 
water. In drawing, a line drawn parallel to the 
top and bottom of the sheet is called horizontal. 

INSCRIBE. — See circumscribe — its opposite. 
INSTRUMENTAL.— By the use of instruments. 



46 



Hawkins' Mechanical Drawing. 



LINE A line has length, only, as A C ; a right line is 

a straight line, the shortest line that can be drawn 
between two points, A C. 

Straight. One which has the same direction 
throughout its entire length. 

Curved. One no part of which is straight. 

Broken. One composed of different successive 
straight lines. 

Mixed. One of straight and curved lines. 

Center. A line used to indicate the center of 
an object. 

Construction. A working line used to obtain 
required lines. 

Dotted. Aline composed of short dashes. 

Dash. A line composed of long dashes. 

Dot and Dash. A line composed of dots and 
dashes alternating. 

Dimension. A line upon which a dimension 
is placed. 



LINE Full. An unbroken line, usually representing 

a visible edge. 

Shadow. A line about twice as wide as the 
ordinary full line. 

A straight line is often called simply a line, 
and a curved line a curve. 

LONGITUDINAL.— In the direction of the length of an 
object. 

MODEL. — A form used for study. 

OBLIQUE. — Neither horizontal nor vertical. 

OBLONQ. — A rectangle with unequal sides. 

OVAL. — A plane figure resembling the longitudinal 
section of an egg ; or elliptical in shape. 

OVERALL.— The entire length. 

PARALLEL Having the same direction and every- 
where equally distant. 

PATTERN. — That which is used as a guide or copy in 
making things. 

Flat. One made of paper or other thin material. 



Hawkins' Mechanical Drawing. 



47 



PATTERN. — Solid. One which reproduces the form 
and size of the object to be made. 

PERIMETER. — The boundary of a closed plane figure. 

PERPENDICULAR— At an angle of 90°. 

PERSPECTIVE — View; drawing objects as they ap- 
pear to the eye from any given distance and situa- 
tion, real or imaginary. 

PLAN. — Plan, horizontal projection and top view have 
the same meaning. 

PLANE FIGURE. — A part of a plane surface bounded 
by straight or curved lines, or by both combined. 

POLYGON A plane figure bounded by straight lines 

called the sides of the poly- 
gon. The least number of 
sides that can bound a 
polygon is three. Polygons 
bounded by a greater num- 
ber of sides than four are ^*S- 39- 
denominated only by the number of sides. 




POLYGON — ^A polygon of five sides is called a Pen- 
tag07i ; of six, a Hexagoti ; of seven, a Heptagon ; 
of eight, an Octagon; of nine, a Nonagon, etc. 

Diagonals of a polygon are lines joining the 
vertices of angles not adjacent. 

The Perifneter of a polygon is its boundary 
considered as a whole. 

The Base of a polygon is the side upon which 
the polygon is supposed to stand. 

The Altitude of a polygon is the perpendicular 
distance between the base and a side or angle 
opposite the base. 

A Quadrilateral is a polygon having four sides 
and four angles. 

A Parallelogram is a 
quadrilateral which has its 
opposite sides parallel. 

The side upon which a ^'S- 4o. 

parallelogram stands and the opposite side are 
called respectively its lower and upper bases. 




48 



Hawkins' Mechanical Drawing. 



POLYGON.— A Rectangle is a paral- 
lelogram having its angles right 
angles. 

A Square is an equilateral 
rectangle, fig. 41. 

A Rhomboid is an oblique- 
angled parallelogram. 

A Rhombus is an equilateral 
rhomboid, fig. 42. 

A Trapezium is a quadrilat- 
eral having no two sides parallel, 
fig- 43- 

A Trapezoid is a quadrilat- 
eral in which two opposite sides 
are parallel, and the other two 
oblique, fig. 44. 




Fig. 44. 



A POLYHEDRON is a solid bounded 
by planes. There are five regu- 
lar solids which are shown in 
figs. 45, 46, 47, 48 and 49. A 
regular solid is bounded by- 
similar and regular plane figures. 

Fig. 45. — The tetrahedron, 
bounded by four equilateral 
triangles. 

Fig. 46. — The hexahedron, 
or cube, bounded by six squares. 

Fig. 47. — The octahedron, 
bounded by eight equilateral 
triangles. 

Fig. 48. — The dodecahedron, 
bounded by twelve pentagons. 

Fig. 49. — The icosahedron, 
bounded by twenty equilateral 
triangles. 



Hawkins^ Mechanical Drawing. 



49 



PRISM. — A solid whose bases or ends are very similar 
plane figures, and whose sides are parallelograms ; 
prisms are called triangular, square, etc., according 
as the bases are triangles, squares, etc. 

PRODUCE. — To continue or extend. 

PROFILE — An outline or contour. 

PROJECTION. — The view of an object obtained upon 

a plane by projecting lines perpendicular to the 

plane. 
QUADRANT. — The fourth part ; a quarter ; the quarter 

of a circle. 

QUADRISECT. — To divide into four equal parts. 

SECTION. — A projection upon a plane parallel to a 
cutting plane which intersects any object. The 
section generally represents the part behind the 
cutting plane, and represents the cut surfaces by 
diagonal lines. 

SECTIONAL. — Showing the section made by a plane. 



SHADOW. — Shade and shadow have about the same 

meaning. 
SOLID. — A solid has three dimensions — length, breadth 

and thickness. 
SPHERE. — A solid bounded by a curved surface every 

point of which is equally distant from a point 

within called the center. . 

SURFACE. — The boundary of a solid. It has but two 

dimensions — length and breadth. Surfaces are 
plane or curved. 

A Plane Surface is one upon which a straight 
line can be drawn in any direction. 

A Curved Surface is one no part of which is 
plane. 

The surface of the sphere is curved in every 
direction, while the curved surfaces of the cylinder 
and cone are straight in one direction. 

The surface of a solid is no part of the solid, 
but is simply the boundary of the solid. It has 
two dimensions only, and any number of surfaces 
put together will give no thickness. 



50 



Hawkins' Mechanical Drawings 



SYMMETRY — Design. A proper adjustment or adap- 
tation of parts to one another and to the whole. 

TRISECT. — To divide into three equal parts. 

TRIANGLE. — A triangle is a polygon having three 
sides and three angles. Tri is a Latin prefix sig- 
nifying three ; hence a Triangle is literally a figure 
containing three angles. 



A Scalene Triangle is one 
in which no two sides are equal. 
See. fig. 50. 



TRIANGLE. 




Fig. 50. 



An Isosceles Triangle is one 
in which two of the sides are 
equal. See fig. 51. 




Kg. 51. 



An Equilateral Triangle is 
one in which the three sides are 
equal. An Equiangular Triangle 
is one having its three angles 
equal. Kn Acute-Angled Triangle 
is one in which each angle is acute. 

A Right- Angled Triangle is 
one which has one of the angles a 
right angle. See fig. 53. 



An Obtuse-Angled Tri- 
angle is one having an 
obtuse angle. Fig. 54. 



Equiangular triangles are also 
and vice versa. 




Fig. 52. 




Fig. 53- 




Fig. 54. 
equal sided, 



Hawkins' Mechanical Drawing. 



51 



VERTICAL — Upright or perpendicular. Vertical and 
perpendicular are not synonymous terms. 

VERTEX. — See Anglf, Quadrilateral, Triangle. The 
vertex of a solid is the point in which its axis in- 
tersects the lateral surface. 

VIEW — See Elevation. Views are called front, top, 
right or left side, back, or bottom, according as 



they are made on the different planes of projection. 
They are also sometimes named according to the 
part of the object shown, as edge view, end view, 
or face view. 

WORKING DRAWING One which gives all the in- 
formation necessary to enable the workman to 
construct the object. 



52 



Hawkins' Mechanical Drawing, 




1 






1 


FREEHAND DRAWING 


1 


^m^'i 




1 ^*'V 




54 



^pee^^and Qrawing. 



A free-hand drawing is executed with the unaided 
hand and eye, without guiding instruments or other 
artificial help. It is necessary to be known that all 
drawing required cannot possibly be done by rule and 
compass, but that some portions must be drawn " free- 
hand," trusting to the eye alone. 

Hence, it is important that the student should be 
able to sketch at sight from objects he may see, or to 
draw roughly, with a piece of chalk or a pencil, pieces 
of mechanism required to be represented. 

Practice in free-hand should go along with mechan 
ical drawing as progress is made, and thus cultivating 
both branches equally. 



" A simple sketch will often," as has been rather 
roughly said, '• express more than yards of talk.'' 

Even a slight sketch refreshes the memory, and in 
the case of the preparation of a complete set of draw, 
ings, with a view to the making of a thoroughly finished 
mechanical drawing, the proper course to pursue is, to 
make a general sketch, letter the various parts for 
reference, and then prepare a series of detailed sketches, 
similarly lettered, and diffuse with dimensions. 

Everyone, whatever his specialty, feels to-day that 
the ability to sketch rapidly and clearly is among the 
absolute necessities for correct and prompt transactions 
of business, in giving and executing orders and doing 
business with persons outside his profession. 



55 



56 



Hawkins' Mechanical Drawing. 



Mistakes and misunderstandings may be averted 
by means of rough sketches taken at the time and 
shown for confirmation ; this also saves assistants from 
getting into trouble, especially if they pin the sketch 
to the order, for reference, in case of the arising of 
any dispute. These are a few of the advantages of 
knowing how to sketch quickly and correctly. 

In " free-hand " any sort of pencil is better than 
none, but there is a considerable advantage in having a 
good serviceable article — a pencil not too soft nor too 
hard, and one which will retain its point for some little 
time. 

Fig. 55 shows the approved position in which the 
pencil should be held while sketching. The pencil 
should be held firmly between the thumb and first 
finger of the right hand ; press the second finger against 
the pencil at the opposite side to the thumb pressure, 
so that the pencil is firmly held by the contact of the 
thumb and two fingers — the third and fourth fingers 
just coming into easy reach of the paper surface — the 



wrist or ball of the hand resting lightly on the surface 
of the work — the arm resting on the desk or drawing- 
board for steadiness. 

The motion of the pencil is produced from the 
movement of the fingers and thumb, principally in the 
vertical strokes, and the horizontal strokes are pro- 
duced by fingers and thumb, combined with a wrist or 
elbow motion ; the oblique lines and curves are pro- 
duced with a free movement, with nothing cramped or 
confined about the finger joints. 

POSITION. 

It should be observed that nothing is more preju- 
dicial to good execution than the habit of leaning over 
the paper, which ought to be placed on a surface suffi- 
ciently inclined to bring every portion equally under 
the eye, thus obviating the necessity of leaning forward. 
All support to the figure should be obtained by resting 
on the left arm, the right being left free for work. By 
attention to these rules that awkwardness of position, 



Hawkins' Mechanical Drawing. 



57 



so detrimental to a good figure, will be avoided. It is 
better to have the light on the left hand, as in this di- 
rection the shadow of the pencil does not interfere with 
the view of the drawing. 



shaving. The lead should not be cut at the same time 
as the wood, but rested on the thumb and pared 
gently aftenvards ; by attention to these directions the 
pencil will be economized. 



HOW TO CUT A PENCIL. 

Hold the pencil firmly in the 
left hand, as in the drawing, 
allowing about an inch to pro- 
ject beyond the fingers, and 
turn it gradually as the knife 
removes the wood. The knife 
should be held so that the blade 
alone projects beyond the 
fingers, and the part of it 
nearest the handle used for cut- 
ting. The pencil should be 
placed against the inside of the 
thumb of the right hand, as in 
the drawing (fig. 56), and the wood removed by slight 




Fig- 56. 



HOW TO DRAW STRAIGHT LINES. 

Before a line is drawn, the point at which it is to 
commence and the point where it is to end, should be 
known ; and let it be distinctly understood that i/it's 
judgment of the eye, and placing of points, should in- 
variably precede the drawing of every line. 

The first effort should, therefore, be to produce a 
line of points exactly parallel with the upper edge of 
the paper, and at equal distances from each other. 
Commence with point A and place the point B care- 
fully level with it, now place a slip of paper against 
these points in the original, mark their distance apart, 
and see if the same proportion has been given in your 
copy ; if not, make the necessary correction. Proceed 
with the next point, examine it, and so on to the end of 



58 



Hawkins' Mechanical Drawing. 



the line. When this is complete, examine each point 
in succession, to try if it is at the same distance from 
the top of the paper ; when this is correct, proceed to 
draw the first level line. Hold the pencil as in the 
drawing, fig. 57, keeping the elbow near the side; 
join ^ to ^ by one light, steady stroke, produced by a 
movement of the wrist, and add stroke upon stroke 
until the line is of the required depth. Continue this 
process to the end of the line of points. Now place 
the point D at the right distance below the A, proceed 
with the points for another line as before, and continue 
the lines until the paper is covered. In producing the 
stroke the pencil should not be jerked, or any stop be 
made between the points, but the movement should be 
even throughout, and it is much better to produce each 
line by several soft strokes, as i/ie repetition of delicate 
lines induces lightness of touch and freedom of hand ; 
and it is also no small advantage that lines thus pro- 
duced are more easily removed by the India rubber, 
should they require correction. 



TO DRAW THE FIRST OBLIQUE LINE. 

Prepare three rows of points down the side of the 
paper, on the left hand ; examine them to see that they 
are at equal distances from the side and from each 
other; hold the pencil as in the drawing, fig. 58, move 
the elbow a little from the side, and join the points A 
and B with one light line, produced by a movement of 
the fingers and thumb, repeating the strokes until the 
line is of the requisite depth ; proceed to join B to G, 
taking care previously to bring the hand a little down 
the paper, as the line from -4 to (7 is too long to be 
produced from one position. When the three rows of 
points are filled, make another set, examine them and 
proceed as before. By these means the paper will be 
covered with oblique lines, and if the points have been 
placed exactly, the sheet will have a neat and regular 
appearance. 

NoTK. — The drawings of hands are introduced to show the 
positions for holding the pencil, and are not intended for copying. 



Hawkins' Mechanical Drawing. 



59 



Kg. 57. 




6o 



Hawkins' Mechanical Drawing. 

A 



/ 




Fig. 58. 



Hawkins' Mechanical Drawing. 



6i 



It is a common, and at the same time highly injur- 
ious habit, to draw this line by a movement of the 
wrist, the fingers remaining rigid. This may be de- 
tected by watching the action of the thumb ; if it bends 
as the line is produced, all is right ; but if it does not 
the wrist is at work. 



TO DRAW THE UPRIGHT OR PERPENDICULAR LINE. 

This line demands the greatest attention, and any 
care bestowed upon it will be amply repaid in the after 
studies. 

Commence by placing a line of points down the 
side of the paper, examine them very carefully to see 
that they are all the same distance from its edge, hold 
the pencil as in the drawing, fig. 59, move the elbow 
well out from the side, and join the points by a move- 
ment of the fingers and thumb. When one line is 
complete, place the points for the next, and examine 
them from the edge of the paper, not from the line just 



drawn. Proceed in this manner until the paper is cov- 
ered. 

There is in most cases a tendency to place the 
points for this line in a slightly inclined direction, as in 
writing, though in some instances the tendency is the 
opposite, a thoroughly correct eye in this respect being 
a rare gift : and it may be useful to suggest that the 
paper be so placed that the line of points to be pro- 
duced may be exactly in front of the eye. 

TO DRAW THE SECX)ND OBLIQUE LINE. 

Prepare three rows of points down the side of the 
paper, examine them for correctness of position, hold 
the pencil as in the drawing, fig. 60, remove the elbow 
as far as possible from the side, and join the points by 
a movement of the fingers and thumb, and contmue the 
exercise until the paper is covered. 

It will be noticed that each change in direction 
of the line to be drawn, has been accompanied with a 



62 



Hawkins' Mechanical Drawing 




Fig 59- 



Hawkins' Mechanical Drawing, 



63 





Fig. 60. 



64 



Ha wki hs' Me cbanical D raw in g • 



corresponding change in the position of the elbow and 
wrist. The following simple rule will assist the mem- 
ory when placing the hand for any given line ; the 
pencil should be held so that it may form a T with the 
line to be drawn : 





For the horizontal line, elbow near 
the side. 



For the first oblique, elbow a little 
removed. 



For the perpendicular, elbow more 
removed. 



For the second oblique, elbow most 
removed. 



Finger and thumb lines. 

r- 



It may also be interesting to notice, with regard to 
the movements by which lines are produced, that they 
are divided into two systems ; the first is that of the 
wrist, which includes the horizontal, and lines in nearly 

the same direction ; 
the second is that of 
the fingers and 
thumb, by which all 
other lines are 
formed. The follow- 
ing diagram exhibits 
the two systems and 
their various lines 
grouped, and it will 
Finger and thumb lines. ^e observed that 

there is a space marked (a) between the two sets, which 
may be considered neutral ground. Lines in this 
direction may be produced by either movement, as 
may be most convenient, but it will always be found 
that these lines are the most trying to the hand. 




Hawkins^ Mechanical Drawing. 



^ 



ON FIGURES FORMED OF STRAIGHT LINES. '"'^'^ 

Before commencing this subject, let it be clearly 
understood that future success will, in a great measure, 
depend upon the amount of care bestowed upon it. 
The aim should be to obtain absolute accuracy, and for 
this end the copies should be tested by the most care- 
ful measurements, and corrected until they are true 
with the originals, but it should be distinctly under- 
stood that these measurements are only to be made 
after the eye and hand have done their best. 

Fig. 66: Place the points ^, -S. Examine them 
to see that they are the same distance apart as in the 
original, and that they are level ; place the point C ex- 
actly under A, and make A C equal in distance to A B ; 



Note. — To some it may appear that too much time and care 
has been bestowed on mere lines, but let it be understood that a 
good system of line drawing is the basis of all education — the 
slightest outline by a hand thus trained has a bold, free and 
masterly character ; and with regard to shading, which is simply 
an aggregation of good lines, it is only by such a practiced hand 
its most charming effects can be produced. 



now place the point D opposite C and under jff ; try 
the distances between each point to see that they are 
the same ; divide each side by a point half way, and 
then draw the lines. 

Fig. 6y : Repeat the last figure and add the 
lines A and £, taking great care that the points for 
them are correctly placed. 

Fig. 68 : Commence with the square as before ; 
then join the half-way points. 

Fig. 69 : After the square is drawn, place the 
points A and Ji at the right height above the half-way 
points, and C, D at the proper distance from the cor- 
ners, then draw the figure. 

Fig. 70 : The greatest care should be taken with 
the squares for this and the following figure, as the 
slightest error in them will destroy the symmetry o£ 
the drawing within ; when the square is completed, join 
the opposite comers, and place on the crossed lines the 
points B, C, D, E; examine these to see that they are 



66 



Hawkins* Mechanical Drawing. 




Fig. 66. 



Fig. 67. 



Hawkins' Mechanical Drawing 



67 




Fig. 68. 



Fig. 69. 



68 



Hawkins' Mechanical Drawing. 




Fig. 70. 



Fig. 71- 



Hawkins' Mechanical Drawing. 



69 



each at the same distance from the centre A, and that 
this distance is equal to the space from A to the sides 
of the square ; when all are proved to be correct, com- 
' plete the figure. 

Fig. 71 : Repeat the last drawing with, if possi- 
ble, greater exactness, and outside the octagon place 
the points A, B, C\ D, etc. ; examine each of these 
points to see that they are all at the same distance 
from the centre, and then complete the figure. 

ON CURVED LINES. 

The right position of the hand for drawing any 
curved line is that required for a straight line which 

would touch the extremities of 
"\N^ the curve. The straight lines 
given in the exercises are valu- 
able, not only as a guide to the 
position of the hand, but as an assistance to the eye 
when forming the curves or examining them after they 
ore produced. 





The direction given for drawing a st r ai g ht line was 
to form it by one steady movement from point to point, 
without any jerk or stop by the way. This instruction 
requires to be changed for the curve, which is better 
produced by several short strokes, thus : ' 

or by overlapping 

lines, any outside bits 

being cleared away 

with India rubber. 

These exercises will test the drawing power and 

try the patience of the pupil, but they are worthy of all 

the care which can be bestowed, which in future efforts 

will meet with its full reward. 

Fig. "jS : Draw first the square as directed in the 
previous lesson, join the points A, B, Cand add the 
short lines at ^and F, proceed with the curve A B, 
drawing it with faint lines at first, and adding stroke 
upon stroke until the required depth is obtained ; the 
curve A (?ls more diflficult to produce, in consequence 
ol the formation ot the hand ; it should, therefore, be 



Jo 



Hawkins' Mechanical Drawing. 




Fig. 76. 



Fig. 77. 



Hawkins' Mechanical Drawing. 



71 



drawn in shorter pieces, joining them together after- 
wards by over strokes. 

Fig. yy : Draw the square and straight 
lines first, then add the curves, taking 
care to give the greatest fullness at the 
right place. 

Fig. 78 : Draw the square and straight 
lines, proceed with the curves, taking care 
to make each of the same proportion. 

Figs. 79 and 80 : The ovals contained 
in these figures are simply foreshortened 
circles, and as such forms are of frequent 
occurrence in sketching from objects, in bridges, 
wheels, ends of timber, etc., they should be carefully 
studied ; the greatest difficulty is to turn the narrow 
ends, and prevent their looking like corners. For this 
purpose it is better to draw the short curves first, thus : 
and then join the longer sides to them. 

Fig. 81 : If this figure can be drawn correctly, a 
great success has been achieved ; the circle is a most 



difficult form to delineate, and without system could 
not be accomplished. Draw the square and straight 
lines within it with great care, examine each point of 
the octagon to see that it is at the same distance from 
the centre, and then draw the circle. 

EXAMPLES FOR PRACTICE, 

Several figures 83 to 96, representing more or less 
familiar parts of machines, utilities, etc., are introduced 
for practice in free-hand, but — 

It must be noted that even in free-hand the wise 
student will occasionally use the straight edge and 
compasses, so as to make his first attempts fairly cred- 
itable. Many good draughtsmen have begun by sim- 
ply copying such figures and illustrations as are used 
throughout this volume and other similar sources ; 
perhaps there is nothing better for practice or training 
than the copying and reproducing of samples of good 
mechanical drawings, yet it must always be remem- 
bered that advancement in free-hand must be made in 



72 



Hawkins' Mechanical Drawing, 





Fig. 78. 



Fig. 79. 



Hawkins' Mechanical Drawing. 



n 




Fig. 80. 



Fig. 81. 



74 



Hawkins' Mechanical Drawing. 



the line of less to greater efforts, and that the why and 
wherefore will be constantly asked by the aspiring stu- 
dent ; that good and correct drawings are to be aimed 
for at all times in every line and dimension — never 
forgetting the law of proportion in the smallest outlines 
of objects to be represented. 

Fig. 83 is a section, or end view of a bar of angle 
iron ; the student will find helpful practice in attempt- 
ing this figure ; he may be allowed to use a straight- 
edge in drawing the lines, but no measurements ; the 
work should be tested on completion by a rule, or 
better by penciling from the original on tracing paper, 
and comparing the free-hand with the copy, when the 
defective proportions, if any, will be clearly exhibited. 

Fig. 84 is a section of tee iron, and fig. 85 is a 
section of channel iron. These three figures on page 
75 should be practiced alternately, although seeming 
similar in shape. 

Fig. 86 is a side and end view of an angle plate 
shaded. Fig. 87 is a wrench shaded. 



Examples of bolt ends are shown in the two next 
numbers ; fig. 88 exhibits the common square-head 
bolt, and fig. 89 the hexagon or six-sided bolt-head ; 
these are also examples of straight-line shading. Fig. 
90 is a lathe-dog, and shows an example of curved 
shading; fig. 92 is an engine crank, and an example of 
straight and curved shading ; fig. 91 is a screw clamp. 

F'g- 93 is a section of boiler plates riveted to- 
gether ; a caulking tool is also shown. 

In the example, fig. 94 — a hand-wheel — the prin- 
cipal difificulty, even for the most advanced student 
in free-hand, will be in drawing the circles ; a coin, if 
convenient, can be used to scribe about, in drawing 
these ; the other parts can afterwards be filled in around 
the circle. Fig. 96 is introduced for practice in pencil- 
ing and shading; the figure represents a water-wheel 
on a stone pier. 

The familiar oil can is shown in fig. 95. These all 
are excellent objects for practice. 



Hawkins' Mechanical Drawing. 



75 






Fig. 83. 



Fig. 84. 



Fig. 85. 






Fig. 86. 



Fig. 87. 



76 



Hawkins' Mechanical Drawing, 




Ifig. 92- 



^- 93. 



Hawkins* Mechanical Drawing, 




Fig. 94- 




77 



-Pi^- 95- 




Fig. 96. 



78 



8o 



Hawkins* Mechanical Drawing. 




G^^ometpieal J^pawing. 



Geometry is the science of measurement ; it has 
been known for more than three thousand years; 
many lives have been devoted to its development, and 
it exists to-day as the foundation of all mathematics. 

Geometrical drawing is the art of representing, to 
the eye, the problems " worked out " by geometricians, 
and the importance of a knowledge of geometrical 
drawing is paramount. The student will find that the 
figures delineated and explained in the next few pages 
constantly occur in mechanical drawing. Says Walter 
Smith, State Director of Art Education in Massachu- 
setts, " I have never known a case where a student did 
not progress more satisfactorily in his studies after a 
course of practical geometry." 



The elementary conceptions of geometry are few : 

I. — ^A point. 

2. — A line. 

3. — A surface. 

4. — A solid, and 

5. — An angle. 
All of which elements are used in mechanical drawings. 

From these, as data, a vast number of mathemat- 
ical problems have been deduced ; of which a few of 
the most elementary will be illustrated in this work ; 
but these few will repay the attention of the student. 

In " freehand " drawing the crayon and pencil 
are used ; in geometrical drawings the dividers, as 



81 



82 



Hawkins' Mechanical Drawing. 



shown in illustration, fig. 97, together with a rule, are 
all that is necessary to accomplish the work. 

A problem is something to be done, and geometry 
has been defined as the science of measurement ; the 
relation between geometry and mechanical drawing 
is very close, hence the term " geometrical problem." 

Before proceeding with the examples, a few 




Fig. 97. 




a\^\\\\u\\\\\^\\\^\\\^^^\^^^^^^\^^^ \^^^\^^\\^^^\^^^\^^^\^^^\^ 
Fig. 98. 

elementary statements belonging to the science of 
geometry are presented ; these will be useful to the 
student, not only while " doing " the problems, but in 
many cases of every-day — future — experience. 



Geometry is one of the oldest and simplest of 
sciences ; it may be defined as i/te science of measure- 
ment ; geometry is the root from which all regular 
mathematical calculations issue. It has claimed the 
best thought of practical men from the times of the 
Greeks and Romans two thousand years ago; they 
derived their knowledge of the science from the Egyp- 
tians, who in turn were indebted to the Chaldeans and 
Hindoos in times beyond any authentic his- 
tory ; hence it was under the operations of 
the laws explained in geometry, that the pyra- 
mids of Egypt and the temples of Greece were 
constructed, as well as the engines of war and 
appliances of peace of ancient times. 

A point is mere position, and has no mag- 
nitude. 

A line is that which has extension in length only. 
The extremities of lines are points. 

A surface is that which has extension in length 
and breadth only. 



Hawkins' Mechanical Drawing. 



83 



A solid is that which has extension in length, 
breadth and thickness. 

An angle is the difference in the direc- 
tion of two lines proceeding from the same 
point. 

Lines, Surfaces, Angles and Solids constitute the 
different kinds of quantity called geometrical magni- 
tudes. 

Parallel lines are lines which have the 

same direction ; hence parallel lines can 
never meet, however far they may be produced ; for 
two lines taking the same direction cannot approach or 
recede from each other. 

An Axiom is a self-evident truth, not only too 
simple to require, but too simple to admit of demonstra- 
tion. 

A Proposition is something which is either proposed 
to be done, or to be demonstrated, and is either a 
problem or a theorem. 



A Problem is something proposed to be done. 

A Theorem is something proposed to be demon- 
strated. 

A Hypothesis is a supposition made with a view to 
draw from it some consequence which establishes the 
truth or falsehood of a proposition, or solves a problem. 

A Lemma is something which is premised, or 
demonstrated, in order to render what follows more 
easy. 

A Corollary is a consequent truth derived imme- 
diately from some preceding truth or demonstration. 

A Scholium is a remark or observation made upon 
something going before it. 

A Postulate is a problem, the solution of which is 
self-evident. 

Let it be granted — 

L That a straight line can be drawn from any 
one point to any other point ; 



84 



Hawkins' Mechanical Drawing. 



II. That a straight line can be produced to any 
distance, or terminated at any point ; 

III. That the circumference of a circle can be 
described about any center, at any distance from that 
center. 

The common algebraic signs are used in Geometry, 
and it is necessary that the student in geometry should 
understand some of the more simple operations of 
algebra. As the terms circle, angle, triangle, hypothe- 
sis, axiom, theorem, corollary and definition are con- 
stantly occurring in a course of geometry, they are 
abbreviated as shown in the following list : 
Addition is expressed by . . . . -(- 

Subtraction « <i ... — 

Multiplication " " . . . . x 

Equality and Equivalency are expressed by . = 

Greater than, is expressed by . . . > 

Less than, " " . . . < 

Thus £ is greater than A, is written . B>A 

B is less than J. " " . . B<A 



A circle is expressed by . 

An angle « " ... 

A right angle is expressed by 

Degrees, minutes and seconds are expressed by 

A triangle is expressed by . 

The term Hypothesis is expressed by . 

" Axiom " " 

Theorem " " . 

" Corollary " « 

" Definition " " . . 

" Perpendicular is expressed by 
The difference of two quantities, when it is not 
known which is the greater, is expressed by 
the symbol ..... 
Thus, the difference between A and B is written A 



. O 

L 

R. L 

a I n 
. A 

(Hy.) 
(Ax.) 
(Th.) 
(Cor.) 
(Def.) 



B 



QEOnETRICAL AXIOHS. 

1. Things which are equal to the same thing are 
equal to each other. 

2. When equals are added to equals the wholes art 
equal. 



Hawkins' Mechanical Drawing. 



85 



3. IVken equals are taken front equals the remain- 
ders are equal. 

4. When equals are added to unequals the wholes 
are unequal. 

5. When equals are taken from unequals the 
remainders are unequal. 

6. Things which are double of the same thing, or 
equal things, are equal to each other. 

7. Things which are halves of the same thing, or 
of equal things, are equal to each other. 



8. The whole is greater than any of its parts. 

9. Every whole is equal to all its parts taken 
together. 

10. Things which coincide, or fill the same space, 
are identical, or mutually equal in all their parts. 

11. All right angles are equal to one another. 

12. A straight line is the shortest distance between 
two points. 

13. Two straight lines cannot enclose a space. 



Problems in Geometpieal |^raw?ing. 




Fig. 99. 



Example i.— To bisect 
(cut in two) a straight line or 
an arc of a circle. Fig. 99. 
From the ends of J. ^ as 
centers, describe arcs cutting 
each other at C and D, and 
draw C D, which cuts the 
line at E or the arc at F. 



Ex. 2. — To draw a perpendicular to a straight line, 
or a radial line to a circular arc. Fig. 99. Operate as 
in the foregoing problem. The line CD is pei-pendic- 



ular to A B; the line C D is klso radial to the arc 
AB. 

Ex. 3. — To draw a 
perpendicular to a straight 
line, from a given point in 
that line, Fig. 100. With 
any radius from any given 
point A in the line B C, 
cut the line at B and C. 
Next, with a longer radius, 
describe arcs from B and <7, cutting each other at D, 
and draw the perpendicular D A. 




Fig. 100. 



86 



Hawkins' Mechanical Drawing. 



87' 




Fig. loi. 



Second Method, Fig. 
loi. From any center F 
above B C, describe a cir- 
cle passing through the 
given point A-, and cutting 
the given line at D ; draw 
D F, and produce it to cut 
the circle at E; and draw 
the perpendicular A E. 




Kg- 103. 



Ex. 4. — To draw a perpen- 
dicular to a straight litie front 
atij point without it, Fig. 103. 
From the point A with a suffi- 
cient radius cut the given line at 
J^and G; and from these points 
describe arcs cutting at E. Draw 
the perpendicular A E. 



Third Met Jiod, Fig. 102. From 
A describe an arc E C, and from E, 
with the same radius, the arc A G 
cutting the other at C ; through C 
draw a line E G D and set off G D 
equal to G E, and through D draw 
the perpendicular A D. 




If there be no room below the line, the intersection 
may be taken above the line ; that is to say, between 
the line and the given point. 



Fig. 102. 



88 



Hawkins' Mechanical Drawing. 



Second Me t hod. 
Fig. 104. From any two 
points B C 3.t some dis- 
tance apart, in the given 
line, and with the radii 
B A, C A, respectively, 
describe arcs cutting at 
A D. Draw the per- 
pendicular A D. 





Fig. 104. 



Ex. 5. — To draw a par. 

allel line through a given 

point, ¥\g. 105. With a radius 

equal to the given point C 

Fig. 105. from the given line A B, 

describe the arc D from B, taken considerably distant 

from C. Draw the parallel through C to touch the 

arc D. 




Second Method, Fig. 106. 
From A, the given point, 
describe the arc F D, cutting 
the given hne at F; from F, 
with the same radius, describe 
the arc ^^, and set off i^Z>, Fig. 106. 

equal to E A. Draw the parallel through the points A D. 

When a series of parallels are required perpendic- 
ular to a base line A B, they may be drawn as in fig. 

107 through points in 
the base line set off at 
the required distances 
apart. This method is 
convenient also where 
a succession of paral- 
lels are required to a 
given line C D, for the 
perpendicular may be 
drawn to it, and any number of parallels may be drawn 
on the perpendicular. 






Fig. 107. 



Hawkins' Mechanical Drawing. 



89 




Fig. 108. 



Ex. 6. — To divide a line into a Jiumber of eqtial 
parts. Fig. 108. 

To divide the 
line A B into, say, 
five parts. From A 
and B draw parallels 
A C, B D on oppo- 
site sides ; set off any- 
convenient distance four times (one less than the given 
number), from ^ on ^ C, and on B on B I; join the 
first on ^ 6' to the fourth on B J), and so on. The 
lines so drawn divide A B as required. 

Second Method, Fig. 109. 
Draw the line at A C, at an 
angle from A, set off, say, five 
equal parts ; draw B 5, and 
draw parallels to it from the 
other point of division in A 
C. These parallels divide A 
Fig. 109. B as required. 




Ex. 7. — Upon a straight line to draw an angle 
equal to a given angle, Fig. I lO. Let A be the given 
angle and F G the line. With any radius from the 
points A and F, describe arcs D F, IE, cutting the 
sides of the angle A and the line F G, 




Fig. no. 
Set off the arc IS, equal to D ^and draw F H. 

The angle F is equal to A 
as required. 



Ex. 8. — To bisect an an- 
gle, Fig. III. Let AC B he 
the angle ; on the center C 
cut the sides at A B. On A 
and B as centers describe arcs 
cutting at D dividing the 
angle into two equal parts. 




Fig. III. 



90 



Hawkins' Mechanical Urawing. 




Fig. 112. 
Ex. lo. — Through two 
given points to describe an 
arc of a circle with a given 
radius, Fig. 113. On the 
points A and B as centers, 
with the given radius, de- 
scribe arcs cutting at C; and 
from Cwith the same radius, 
describe an arc ^ ^ as re- 
quired. 



Ex. 9. — To find 
the center of a circle 
or of an arc of a cir- 
cle. Fig. 112. Draw 
the chord A B, bisect 
it by the perpendic- 
ular C D, bounded 
both ways by the cir- 
cle ; and bisect CD 
for the center G. 





Fig. 114. 



Fig. J13. 



Second, for a circle or 
an arc, Fig. 1 14. Select three 
points A, B, C in the cir- 
cumference, well apart ; with 
the same radius describe 
arcs from these three points 
cutting each other, and draw 
two lines D E, FG, through 
their intersections according 
to Fig. 107. The point where 
they cut is the center of the circle or arc. 

Ex. II.— 7^7 describe a circle passing through three 
given points, Fig. 1 14. Let A,B,C be the given points 
and proceed as in last problem to find the center O, 
from which the circle may be described. 

This problem is variously useful ; in finding the 
diameter of a large fly-wheel, or any other object of 
large diameter when only a part of the circumference 
is accessible ; in striking out arches when the span and 
rise are given, etc. 



Hawkins' Mechanical Drawing. 



91 




Ex. 12. — To draw a tangent to a circle from a given 
point in the circumference, Y\g. 115. From ^ set off 

equal segments A B, 
A D, join B D and 
AxdiW AE, paiallel to 
it, for the tangent. 



Ex. 13. — To 
draw tangents to a 
circle from points 
without it. Fig. 1 1 6. 
From A with the 
radius A C describe 
an arc BCD, and 
from Cwith a radius 
equal to the dia- 
meter of the circle, 
cut the arc at B D, 
join B C, CD, cut- 
ting the circle at E F, and draw A E, A F, the tangents. 




Ex. 14. — Between two inclined lines to draw a series 
of circles touching these lines and touching each other, 
Fig. 117. Bisect the inclination of the given lines AB, 
CD by the line if 0. From a point P in this line draw 
the perpendicular F B to the line A B, and on P de- 




Jig. 116- 



Fig. 117. 

scribe the circle B D, touching the lines and cutting the 
center lines at E. From ^draw ^'i^ perpendicular to 
the center line, cutting A B at F, and from J^ describe 
an arc E G, cutting ^ ^ at G. Draw G II parallel to 
B P, giving n, the center of the next circle, to be de- 
scribed with the radius HE, and so on for the next 
circle, / iT. 



92 



Hawkins' Mechanical Drawing. 




Fig. ii8. 



Ex. 15. — To construct a tri- 
angle on a given base, the sides 
being given. 

First. An equilateral triangle, 
Fig. 118. On the ends of a given 
base A B, with ^ ^ as a radius 
describe arcs cutting at C, and 
draw^ C C B. 

Second. Triangle of unequal sides, Fig. 119. On 
either end of the base A D, with the side ^ as a radius 
describe an arc; and with the side (7 as a radius, on 
the other end of the base as a center, describe arcs cut- 
ting the arc at E\ join A E, 
D E. 

This construction may be 
used for finding the position 
of a point G or E at given 
distances from the ends of a 
base, not necessarily to form 
Fig. 119. a triangle 




Ex. 16. — To construct a 
square rectangle on a given 
straight line. 

First. A square, Fig. 
120. On the ends B Az.?, 
centers, with the line A B 
as radius, describe arcs cut- 
ting at (7; on (7 describe 
arcs cutting the others at 
D E; and on Z> and E cut these at E G. 
AE, B G and join the intersections HI. 




Fig. 120. 



Draw 




Fig. 121. 



Second. A rectangle, Fig, 
121. On the base ^i^ draw the 
perpendiculars EH, F G, equal 
to the height of the rectangle, 
and join G H. 



Hawkins' Mechanical Drawing. 



93 




Fig. 122. 



Ex. 1 7. — To construct a 
parallelogram of which the 
sides and one of the a?tgles 
are given, Fig. 122. Draw 
the side D E equal to the 
given length A, and set off 
the other side D F equal to 
the other length S, form- 
ing the given angle C. From E with D F as radius, 
describe an arc, and from F, with the radius D E cnt 
the arc at G. Draw F G, E G. Or, the remaining 
sides may be drawn as parallels to D E, D F. 

Ex. 18. — To describe a 
circle about a triangle, Fig. 
123. Bisect two sides A B, 
AC oi the triangle at E F, 
and from these points draw 
perpendiculars cutting at K. 
On the center K, with the 
radius K A draw the circle 
Fig. 123. ABC. 




Ex. 19. — To describe a circle about a square, and 
to inscribe a square iti a circle. Fig. 124. 



First. To describe the circle. 
Draw the diagonals A B,C D oi 
the square, cutting at E; on the 
center E with the radius E A 
describe the circle. 




Fig. 124. 



Second. To inscribe the square. Draw the two 
diameters AB, C D at right angles and join the points 
A B, C D to form the square. 

In the same way a circle m.ay be described about a 
triangle 



94 



Hawkins' Mechanical Drawing, 



Ex. 20. — To inscribe a circle on a square, and to 
describe a square about a circle, Fig. 125. 

First. To inscribe the circle. Draw the diagonals 
A B, CD of the square, cutting at E\ draw the per- 
pendicular E jF to one side, and with the radius E F 
describe the circle. 




Fig. 125. 

Second. To describe the square. Draw two di- 
ameters A B, C D a.t right angles, and produce them ; 
bisect the angle D E B zX the center by the diameter 
F G, and through J^and G draw perpendiculars A C, 
B D, and join the points A D and B C where they 
cut the diagonals to complete the square. 



^H 



Fig. 126. 



Ex. 2 1 . — To iti- 
scribe a circle ifi a 
triangle, Fig. 126. 
Bisect two of the 
angles ^ <7 of the 
triangle by lines 
cutting at D ; from 
D draw a perpendicular D E to any side, and with 
D E as radius describe a circle. 

Ex. 22. — To inscribe a pentagon in a circle. Fig. 1 27. 
Draw two diameters A C, B D 2X right angles cuttmg 
at O; bisect A O aX. E, and 
from E with radius E B cut 
A C at F, and from B with 
radius B F cut the circum- 
ference at G H and with 
the same radius step round 
the circle to /and K; join 
the points so found to form 

the pentagon. „. 

^ - Fie. 127. 




Hawkins^ Mechanical Drawing. 



95 




Ex. 23. — To construct 

a hexagon upon a given 

straight line. Fig. 128. 

From A and B, the ends 

of the given Hne, describe 

arcs cutting at G ; from G 

with the radius G A de- 
scribe a circle. With the 

same radius set off the 

arcs A C, C F and B D, Fig. 128. 

D E\ join the points so found to form the hexagon. 
Ex. 24. — To inscribe a hexag07i in a circle. Fig. 129. 

Draw a diameter A C B ; 
from A and B as centers, 
with the radius of the cir- 
cle A Ccut the circumfer- 
ence at D, E, F, G, and 
draw A B, D F, etc., to 
form the hexagon. The 
points D F, etc., may be 
found by stepping the 
radius (with the dividers) 
Fig. 129. six times round the circle. 





Pig. 130. 



Ex. 25. — To describe an 
octagon on a given straight 
line. Fig. 1 30. Produce the 
given line A B both ways 
and draw perpendiculars 
A F, B F; bisect the ex- 
ternal angles A and B by 
the lines A II, B C, which 
make equal to A B. Draw 
CD 2m6.II G parallel to 
A F and equal to A B ; 
from the center (?/), with the radius^ ^, cut the perpen- 
diculars at F F, and draw F F to complete the hexagon. 

Ex. 26. — To convert a 
square into an octagon. Fig. 
131. — Draw the diagonals 
of the square cutting at F; 
from the corners A, B,C,D, 
with ^ ^ as radius, de- 
scribe arcs cutting the 
sides at G, H, etc., and 
join the points so found 
to complete the octagon. 




96 

Ex. 27. — To inscribe 
an octagon in a circle. Fig. 
132. Draw two diameters 
A C, B D, at right angles ; 
bisect the arcs A B, B C, 
at E, F, etc., to form the 
octagon. 



Hawkins' Mechanical Drawing. 






Fig. 132. 



Ex. 28. — To describe 
an octagon about a circle, Fig. 133. Describe a square 

about the given z\xc\q.AB, 
draw perpendiculars II 
and K, to the diagonals, 
touching the circle to form 
the octagon. Or, the points 
II, K, etc., may be found 
by cutting the sides from 
the corners, by lines paral- 
Fig- 133- ^^ t° ^^ diagonals. 




■■ 



Ex. 29. — To describe an ellipse when the length and 
breadth are given. Fig. 134. On the center C, with^ E 
as radius, cut the axis A B 2X i^and G, the foci, fix 
a couple of pins into the axis at F and G, and loop on a 
thread or cord 
upon them 
equal in length 
to the axis ^^, 
so as when 
stretched to 
reach the ex- 
tremity C of 
the conjugate 
axis, as shown 
in dot-lining. 
Place a pencil 
or drawpoint *^' ^^' 

inside the cord, as at H, and guiding the pencil in this 
way, keeping the cord equally in tension, carry the 
pencil round the pins F, G, and so describe the ellipse. 

Note. — The ellipse is an oval figure, like a circle in per- 
spective. The line that divides it equally in the direction of its 
great length is the transverse axis, and the line which divides the 
opposite way is the conjugate axis. 



Hawkins' Mechanical Drawing. 



97 



Second Method. Along the straight edge of a 
piece of stiff prper mark off a distance a c equal to 
A C, half the transverse axis ; and from the same point 
a distance a b equal to CD, half the conjugate axis. 
Place the slip so as to bring the point b on the line A B 
of the transverse axis, and the point c on the line 



D E ; and set off on the drawing the position of 
the point a. Shifting the slip, so that the point 
travels on the transverse axis, and the point c on 
the conjugate axis, any number of points in the curve 
may be found, through which the curve may be traced. 
See fig. 135. 




Fig. 135. 



T^pigonometpjf. 



Trigonometry is that portion of geometry which 
has for its object the measurement of triangles. When 
it treats of plane triangles, it is called Plane Trig- 
onometry ; and as the engineer will continually meet 
in his studies of higher mathematics t]ie terms used 
in plane trigonometry, it is advantageous for him 
to become familiar with some of the principles and 
definitions relating to this branch of mathematics. 

The circumferences of all circles contain the same 
number of degrees, but the greater the radius the 
greater is the absolute measures of a degree. The 
circumference of a fly wheel or the circumference of 
the earth have the same number of degrees ; yet the 
same number of degrees in each and every circumfer- 
ence is the measure of precisely the same angle. 

The circumference of a circle is supposed to be 



divided into 360 degrees or divisions, and as the total 
angularity about the center is equal to four right 
angles, each right angle contains 90 degrees, or 90°, 
and half a right angle contains 45°. Each degree is 
divided into 60 minutes, or 60'; and for the sake of still 
further minuteness of measurement, each minute is 
divided into 60". In a whole circle there are, therefore, 
360x60x60=1,296,000 seconds. The annexed dia- 
gram, fig. 136, exemplifies the relative positions of the 



Sine, 

■ Co-sine, 

Versed Sine, 

of an angle. 

These may be defined thus ; 



Tangent, 

Co-Tangent, 
Secant and 

Co-secant 



98 



Hawkins' Mechanical Drawing. 



99 




Fig. 136. 

DEFINITIONS. 

1. The Complejnent of an arc is 90° minus the arc. 

2. The Supplement of an arc is 180° minus the arc. 

3. The Sine of an angle, or of an arc, is a line 
drawn from one end of an arc, perpendicular to a dia- 
meter drawn through the other end. 

4. The Cosine of an arc is the perpendicular dis- 



tance from the center of the circle to the sine of the 
arc ; or, it is the same in magnitude as the sine of the 
complement of the arc. 

5. The Tangent of an arc is a line touching the 
circle in one extremity of the arc, and continued from 
thence, to meet a line drawn through the center and 
the other extremity. 

6. The Cotangent of an arc is the tangent of the 
complement of the arc. The Co is but a contraction of 
the word complement. 

7. The Secant of an arc is a line drawn from the 
center of the circle to the extremity of the tangent. 

8. The Cosecant of an arc is the secant of the 
complement. 

9. The Versed Sine of an arc is the distance from 
the extremity of the arc to the foot of the sine. 

For the sake of brevity, these technical terms are 
contracted thus : for sine A B, we write sin. A B ; for 
cosine A B, we write cos. A B ; for tangent A B, we 
write tan. A B, etc. 



lOO 



Hawkins' Mechanical Drawing, 



The circle is a plane figure comprehended by a 
single curved line, called its circumference^ every part 
of which is equally distant from a point called the 
center. Of course, all lines drawn from the center to 
the circumference are equal to each other. 

.7854 

" Why is the decimal .7854 used to ascertain the 
area of a circle or round opening?" is a question fre- 
quently asked. Now, if you will divide a square inch 
into 10,000 equal parts, then describe a circle one inch 
in diameter and divide that into ten-thousandths of an 
inch, as shown in illustration, you will find that you 
have 7854 of such squares, each one thousandth of an 
inch; hence the decimal .7854 is used as a "constant" 
or multiplier, after squaring the diameter, and the re- 
sult is the area of the circle. 

3.1416 

The Greek letter n-, called pi, is used in mathe- 



matical calculation to represent 3.1416, nearly. Another 
approximate proportion is ^-^ and another still nearer 



is 



The number 3.1416 is the circumference of a circle 
represented by the figure one ; it may be one inch, one 
foot, or one mile. The area of this same figure (i) is 
.7854, as explained above. Calculations relating to 




«--— lin. 



10.000 
PARTS. 



circles are almost without number; to aid in solving 
these problems quickly and accurately tables have 
been figured, proved and arranged in convenient form 
for ready reference. These tables will be found begin- 
ning on page 273. 



f^V^^H 








INSTRUMENTS 

AND 

MAIERIALS 




^ita^^H 


^^^^^^^^^^^^^^^^^^^^^H^^^^I^^^^^^^^^^^^^^^^^^^^^^^^B^^^^^^^^^^^^^' ^^^^^^^^1 






Fig- 137. 



Qpawing TVl^terials and Instruments. 



Drawing tools or instruments are contrived solely 
for mechanical drawing ; aside from this use they are 
perfectly worthless, hence the quality of these special 
utensils is a matter of the first consideration to the earn- 
est student. 

There are several degrees of excellence to be found 
in the make-up of drawing instruments and materials ; 
it may be remarked with truth that " any kind are good 
enough, and the best none too good," i. e., a learner in 
this delightful art should not stop at the lack of good- 
ness or the low grade existing in his " tools," but 
rather do the best work possible with the means at 
hand. 

However, in order that acceptable work may be 
accomplished, fairly good instruments should be pro- 



cured. The advice of some one experienced in the use 
and care of draughting tools should be sought before 
purchasing. A drawing board, a single sheet of paper 
and a pencil is the simplest " outfit " to be thought of; 
to this small beginning may be added, soon afterwards, 
an inexpensive pair of compasses, a T-square and a 
couple of triangles ; a vast range of work can be exe- 
cuted with these few tools. 

Nothing else will be needed to do fine work 
except, perhaps, one or two pairs of better com- 
passes and a few sweeps or means of drawing irregular 
curves ; all these had best be purchased separately ; for 
in buying a " box of instruments," it may contain some 
articles which are not desired, or that are of a wrong 
size, or even duplicates of those already possessed. 



103 



I04 



Hawkins' Mechanical Drawing. 



An outfit recommended by the author of " Reed's 
Hand Book " is as follows. 

Large compasses with 
movable leg. 

A pair of dividers. 

Bow pencil. 

Bow pen. 

Pencil leg for large com- 
passes. 

Pen leg for large com- 
passes. 

Drawing pen. 




Fig. 138. 



Louis Rouillon, B. S., Instructor of Drawing in 
Pratt Institute, New York, recommends the follow- 
ing: 

Compasses, 5)^ inches, with needle point; pen, 
pencil and lengthening bar. 
Drawing pen, 4^ inches. 
T-square, 24-inch blade. 



45-degree triangle, 9 inches. 

30 and 60 degree triangle, 9 inches. 

I Scroll. 

Dixon's V. H. pencil. 

12-inch boxwood scale, flat, graduated 1-16 inch 
the entire length. 

Bottle of liquid India ink, four thumb-tacks, pen 
and ink eraser. 

20 sheets drawing paper, 11X15 inches, and a 
drawing-board about 16x23 inches will also be neces- 
sary ; students can usually make the board themselves 
for less money than it can be bought. 

NoTB. — The purchasing of drawing tools is one of the most 
diflBcult points to settle that can present itself to a person about to 
buy a drawing outfit for the first time. Nothing can be so produc- 
tive of distress to a person drawing as to have his tools getting out 
of order, joints one day too tight, next day too slack, points get- 
ting blunt or perhaps turning up altogether ; if needle points, then 
the needles slip up, and drawing spoiled ; in fact, the purchaser 
can be annoyed in numberless different ways.— W. H. Thorn. 



Hawkins* Mechanical Drawing, 



105 




Kig. 139- 



io6 



Hawkins' Mechanical Drawing 




Fig. 140. 



Hawkins' Mechanical Drawing. 



107 



THE DRAWING BOARD. 

A drawing-board should be made of well seasoned 
pine of a convenient size, say 23X 16, which will take 
half a sheet of imperial paper, leaving j4-inch margin 
all around. 

The working surface of the board — or its front 
side — should be perfectly smooth, but instead of being 
flat it should have a very slight camber, or rounding, 
breadthways, this latter feature in its construction 
being to prevent the possibility of a sheet of paper 
when stretched on its surface having any vacuity 
beneath it. 

The four edges of the board need not form an 
exact rectangle, as much valuable time is often wasted 
in the attempts to produce such a board ; but it will 
answer every purpose of the draughtsman so long as 
the adjacent edges at the lower left-hand corner of it 
are at right angles, or square to each other. 

An English authority recommends the use of two 
drawing-boards, 42 inches long and 30 inches wide, 



made of plain stuff, without cleets, l^ inches thick — 
seasoned — with edges perfectly straight and at right 
angles to each other. With tivo boards, one may he 
used for- sketching and drawing details and the other for 
the finished drawing. 

The board should be % inch in thickness, and 
fitted at the back, at right angles to its longest side, 
with a couple of hardwood battens, about 2 inches wide 
and y^ inch thick ; the use of these battens being to 
keep the board from casting or winding and to allow 
of its expansion or contraction through changes of 
temperature. This latter purpose, however, is only 
effected by attaching the battens to the back of the 
board in the following manner : ... At the mid- 
dle of the length of each batten — which should be one 
inch less than the width of the board — a stout, well- 
fitted wood screw is firmly inserted into it, and made to 
penetrate the board for about % inch, the head of the 
screw being made flush with the surface of the batten ; 
on either side of the central screw, two others, about 



io8 



Hawkins' Mechanical Drawing, 




Fig. 141. 



Hawkins' Mechanical Drawing, 



109 



3^ inches apart, are passed through oblong holes in 
the battens, and screwed into the body of the board 
until their heads are flush with the central one ; fitted 
in this way the board itself can expand or contract 
lengthwise or crosswise, while its surface is prevented 
from warping or bending. 

A further improvement in such a drawing board 
as above shown is made by cutting lengthwise along its 
ends a narrow groove and inserting an ebony or hard- 
wood strip ; this is cut or sawn apart at about every 
inch to admit of contraction ; this strip serves as a guide 
to the stock of the drawing square, allowing an easy 
sliding movement. 

To produce really good work in the shape of a 
mechanical drawing, one perfect straight edge only is 
required on a drawing board, and that the left one, 
which is always known as the working-edge; but for 
the convenience of being able to draw a long line across 
the board at right angles to its lower edge, this edge is 



made truly square with that on the left side of the 
board. 

The details for building these drawing boards are 
given, because they are easy to be made by one who 
understands the use of a few wood-working tools ; while 
the boards themselves are difficult of transportation — 
in case of the change of residence of their owners — 
quite unlike the instruments which are to accompany 
them. 




Fig. 142. 

Fig. 141 represents the board which has been de- 
scribed in the text, with provisions for the contraction 
and expansion ; the very dark lines are intended to 
represent the ebony insertions — as described. Fig. 140 
represents a plain pine board with dovetailed battens. 



IIO 



Hawkins' Mechanical Drawing. 



Fig. 142 represents the common means used to at- 
tach or secure slightly or temporarily the drawing paper 




Fig. 143- 




Fig. 144. 

to the drawing board ; these are called thumb-tacks, 
and are usually forced through the paper into the wood 



by the hand, whence they are easily detached. These 
are made to have as slight a projection as may be, so as 
not to interfere with the free movement of the tee- 
square. 

For mechanical drawing the invariable practice is 
to secure the paper on which the drawing is to be made 
to the drawing board by pinning it ; this is effected by 
various kinds of dratuitig pins or thumb-tacks. 

The best kind for this purpose have a head as 
thin as possible without cutting at its edges, slightly 
concave on the under side next the paper, and only so 
much convex on its upper side as will give it suf!icient 
thickness to enable the pin to be secured to it ; better 
use four or more small pins along the edge of a sheet 
of paper, than use one clumsy, badly made pin at each 
end. 

Fig. 143 and fig. 144 represent a pair of plain 
trestles or horses in common use for supporting large 
size drawing boards. This pattern is found frequently 
in the laying-out shop. Fig. 145 and fig. 146 repre- 



Hawkins' Mechanical Drawing. 



Ill 



sent adjustable horses or trestles — these are designed, 
primarily, for office use. As will be seen by viewing the 
illustration, the upper part is supported by two hard- 




Fig- 145- 



Fig. 146. 



wood sliding pieces ; these are provided with strong 
pins and numerous holes, and pass through the frame 
of the trestle, as shown, so that the upper portions can 
be arranged at any angle convenient to the draughts- 
man, as he lies over his work or stands by it. 

Fig. 1 37 is introduced to exhibit the paper attached 
to the drawing board with the thumb-tacks, and with 
the T-square and set-squares arranged to commence 



work ; the paper should not extend to the edges of the 
board; three, four or more tacks may be used on 
each edge of the sheet of paper, instead of two, as shown 
in illustration. 




Fig. 147. 

A most convenient — and except for its extreme 
lightness, which is not good in a drawing stand — a 
most admirable device is shown in fig. 138. The draw- 
ing table is simply a drawing board with folding legs ; 
these are made from hard-wood, while the top is made 



112 



Hawkins' Mechanical Drawing. 



of soft, seasoned pine, with square corners ; while the 
device is strong and well braced, it can be folded and 
easily carried about — all as shown in the illustration. 




Pigs. 149 



THE TEE=SQUARE. 

This is an instrument in the form of a letter T, as 
shown in the figures 149 and 150; the two parts are 
known as stock and d/ade ; the horizontal part of the 
letter (T) is the stock, and the vertical part the blade 
— hence the name, T-square ; to form the square, 
the two parts are joined together in such a way as to 
make them exactly at right angles to each other ; the 
stock, which is applied to the working edge of the 
drawing board, being about one-third the length of the 
blade, and about three times its thickness. 

To be perfect in construction, a tee-square should 
be as light as is consistent with its necessary strength 
and stiffness of parts ; it should be made of suitable 
material easily manufactured, put together, and re- 
paired, and withal as truly correct as is possible to be 
made. Such a square is represented in fig. 148 ; it 
has a taper blade, which is generally about double 
the width where secured to the stock as it is at the 
end. 



Hawkins' Mechanical Drawing. 



"3 



The manner in which the stock is united to the 
blade determines its adaptability or otherwise to the 
use made of it ; in some the stock is rectangular in sec- 
tion, and the blade mortised into it ; in others the 
blade is dovetailed and let into the stock for the whole 
of its thickness. 

ADJUSTABLE BLADED SQUARE. 

In cases where many parallel lines have to be 
drawn, of lengths beyond the capabilities of ordinary 
set-squares, and in directions other than square with or 
parallel to the working edge of the drawing board it is 
convenient to have for use an adjustable bladed tee- 
square, or one whose blade can be set at any desired 
angle. The blade of such a square should be tapered 
as in illustration, but shaped at its wide end as shown, 
and having a stock wide enough to allow for the sur- 
face required in the washers of the fittings necessary to 
make the blade adjustable. These fittings, though re- 
quiring to be well made and neatly finished, are not 



expensive or difficult to make, as they consist merely 
of two washers, a square-necked bolt, and a fly nut. 

The tee-square, as 
shown, has four parts: i, 
blade ; 2, fixed head ; 3, 
shifting head ; 4, swivel. 
The head is held firmly 
by the left hand to the left 
edge of the drawing board, 
and the blade serves as a 
straight-edge for horizon- 
tal lines that may extend 
the whole length of the 
paper. It can be used for 
either horizontal, or, by 
reversing to the bottom of 
the board, for vertical 

lines ; and, by turning it 
Figs. 151 and 152. ^^g^_ g^ ^j^^^ ^1^^ shifting 

head is against the edge of the drawing board in- 




114 



Hawkins' Mechanical Drawing. 



stead of the fixed head, lines at different angles may 
be drawn. The length of the blade should be the length 
of the drawing board ; if it is shorter, inconvenience will 
be experienced when lines the whole length of the 
board are wanted. 




Fig- 153- 



Fig. 154- 



Fig. 155. 



Fig. 156. 



TRIANGLES, OR SET-SQUARES. 

Set-squares are invariably used in connection with 
the tee-square, as shown in fig. 148. The illustrations 
below show several patterns of the device ; by these, 
vertical lines, triangles, squares and hexagonal, octag- 
onal and twelve-sided figures, diagonal section lines, 
etc., can be easily drawn. For ordinary purposes, a 
triangle or set-square with angles of 45° may be 4 



inches long and the other 8 inches in length, but a 
six-inch set-square having angles 90°, 45° and 45°, 
and an eight-inch one having angles of 90°, 60° and 
30°, will be found sufficient for all purposes ; there are 
other triangles used specially for making letters. 

In practice the triangles or set-squares are slid 
along the edge of the blade, and need not be any 
thicker than it. 



PARALLEL RULE. 

This instrument is used to mark lines which are 
neither horizontal nor vertical (usually these are drawn 
by the square and set-square), and which are parallel 
to one another; by adjusting the edge of the parallel 
ruler to a line, it can be extended or opened out (or 




Fig. 157. 



Hawkins^ Mechanical Drawing. 



115 



vice-versa closed), and the line or lines drawn will be 
parallel or equally distant from the base or first line it 
was set by. See fig. 157. 



Fig. 158 is a parallel ruler, constructed with two 
rollers fixed on a rod so, that they move the same 
distance, carrying the ruler parallel to the starting line. 




Fig. 158. 



Note. — It has been said that " a workman may be known by his tools," but the statement mast be taken with a good deal of allow- 
ance. Some workmen may possess a very fine set of tools and never use them, because they have not the abiUty or inclination to learn 
how ; especially is this the case with drawing instruments. 

If all the fine sets of drawing instruments that are owned by workmen were put to freqent use the owners would find a marked im- 
provement in their abilities in other lines as well as drawing ; for it is a noticeable fact that when a person's mind has been trained in a 
business that requires close calculation and a knowledge of materials, he is capable of showing good qualifications in other lines, and the 
more skilled he is in one the easier can he acquire skillfiilness in another, if he applies the same amount of energy, thought and interest 
as he did to acquire skill in the first 



ii6 



Hawkins' Mechanical Drawing, 



SECTION LINER. 

Fig. 1 59 shows an improved section liner which can 
be adjusted to any angle, and will space the parallel 
lines at any desired regular distance. 




Fig. IS9. 



Hawkins' Mechanical Drawing. 



117 



IRREGULAR CURVE OR SCROLL. 

Irregular curves, or, as they are sometimes termed, 
sweeps, represented by figs. 160-166, are used for curves 
that cannot be put in by the other instruments. They 
are very useful when elliptical or parabolic curves are 
desired, in preference to circles or arcs of a circle. 
They are much used in design and architectural draw- 
ing. They are made of thin hardwood or rubber, and 
sometimes of horn. 





Figs. 160-16^ 



ii8 



Hawkins' Mechanical Drawing. 



Curves are irregular lines ; a circle is a regular line. 
If a curve is to be passed through a number of prede- 
termined points it should be first sketched in lightly, 
free-hand ; a section of the scroll is then applied to the 
curve so as to embrace as many points as possible ; 
only the central points of those thus embraced should 
be inked in ; this process is continued until the desired 
curve is completed. 

Curves are made of various material, pearwood, 
cardboard, xylonite, hard rubber, and a strip of soft 
lead is sometimes used, which may be easily adjusted 
to the curve required. 

The curves generally used in mechanical drawing 
are shown on previous page. 

Fig. 208, page 134, is a logarithmic spiral curve. 
It is mathematically constructed and contains every 
curve within the limit of its size. 

ELLIPSES. 

An ellipse is a geometrical figure, and can be 
drawn as described in geometrical problem 29, page 



96; many drawing offices keep sets of hard rubber 
ellipses, to economize time constructing them. 

DRAWING PENCILS. 

These are instruments for marking, drawing or 
writing, formed of graphite, colored chalk or materials 
of similar properties, and having a tapering end, 
inclosed, generally, in a cylinder of 
softwood. Fig. 167 represents a 
ruling pencil ; its point is a paral- 
lelogram or of a wedge shape. In 
ruling, the length view rests against 
the square ; its shape gives con- 
siderable strength to the lead and 
allows the making of a very fine 
line. Fig. 168 differs in the point 
of the pencil shown, as may be 
observed in the illustration. 

A pencil that is hard is best 
for mechanical drawing ; one that 
will retain a good point for some Fig. 167. Fig. 168. 



Hawkins' Mechanical Drawing. 



119 



Fig. 170. 



considerable time. Pencil lines 
should be made as light as possible; 
the presence of lead on the sur- 
face of the paper tends to prevent 
the ink passing to the paper, and 
in rubbing out pencil lines the ink 
is reduced in blackness, and the 
surface of paper is roughened, 
which is a disadvantage. As little 
erasing or rubbing out as possible 
should be done. 



DIVIDERS AND COHPASSES. 

These instruments, while they 
appear alike, have a separate use ; 
the dividers are used to space off 
distances and dimensions ; especi- 
ally are they necessary in reading 
drawings made to scale. Com- 




Fig. 169. 



passes are used for describing circles, curves, etc., dividers 
are used for marking out spaces. 

Two forms of the dividers are shown in figs. 169 
and 170; the simplest, plainest form is shown in fig. 
169; these are used for rough spacings ; fig. 170 repre- 
sents a pair of dividers fitted with an adjustable screw 
controlled by a steel spring in one leg ; by this a very 
exact measurement can be made. Fig. 170 is intended 
to exhibit what is called a " hair-spring divider." 

PROPORTIONAL DIVIDERS. 

These dividers differ from the ordinary ones 
shown in figs. 169 and 170 in that they are provided 
with four steel points, one pair of which being set to 
the full dimension will be reproduced by the other 
pair, but in a smaller, or reduced size. 

Fig. 171 are "bisecting" dividers, being propor- 
tional dividers, which, when open, one end measures 
double the distance of the other. 

Fig. 172 are proportional dividers; the points at 



I20 



Hawkins' Mechanical Drawing. 



Fig. 171. 




Fig. 172 



Fig- 173- 




Fig. 174- 




Hawkins^ Mechanical Drawing. 



121 



one end are capable of being changed, 
to measure practically any desired 
proportion at the other end, by 
altering the position of the pivot 
where the legs cross one another. 
The lower connecting link is a 
micrometer adjustment, for minute 
measurements. 

Fig. 173 are proportional dividers 
which are marked for the proportions 
of lines and radii of circles, being 
provided with a rack movement for 
adjustment. 



Fig. 176. Fig. 174 represents three-leg div- 

iders, used for taking the position of 
three points ; this instrument is very 
useful in finding the position of a point in a 
figure. 



11 



Fig. 175. 



COMPASSES. 

Compasses consist of two 
pointed legs ; they are instruments 
for describing circles or for — 
sometimes — measuring figures, in 
absence of dividers. Fig. 175 
represents compasses fitted a? 
dividers. 

Compasses should have jointed 
legs, which will allow the points 
to be placed at right angles to the 
paper, whatever the size of the 
179. circle to be drawn. Compasses 
should not be used for circles 
which are too large to allow the points to be thus 
placed ; a lengthening bar is generally provided, which 
greatly increases the diameters of circles which may be 
drawn by this attachment ; it is shown in fig. 176. 

One leg of the compasses is usually provided with 
a socket to which are fitted three points : a divider 
point, fig. 179; a pencil point, fig. 177; and a point, 




Fig. 177. 178. 



122 



Hawkins' Mechanical Drawing. 



fig. 178, carrying a special pen for the inking of circles. 
Each of these points is generally provided with a joint, 
so that it may be placed at right angles to the paper. 
The other leg should be jointed ; it is often pro- 
vided with a socket which receives 
two points, one a divider point, and 
the other carrying a needle point. 
Such an instrument may be used as 
dividers for spacing, or as compasses 
for penciling or inking circles. 

The joint at the head of the 
compasses (see fig. 175) is the most 
important feature. It should hold the 
legs firmly in any position, so that in 
going over a circle several times only 
one line will result. It should allow 
the legs to move smoothly and evenly, 
and should be capable of adjustment. 

As shown in fig. 174, one leg has 
Fig. 180. Fig. 181. a hinge or joint, and a needle point, 







Fig. 182. 



Fig. 183. 



Fig. 184. 



Hawkins' Mechanical Drawing, 



123 



which can be regulated by a thumb screw ; the other 
leg has a socket or recess into which interchangeable 
parts can be inserted. The four figures to the right of 
the compasses show the parts which are provided with 
shanks or insertion pieces. Fig. 180 and fig. 181 repre- 
sent compasses specially used for making small circles, 
and work too minute for the larger instruments de- 
scribed above. 

To do work of this nature easily a pair of spring 
dividers are frequently used. This instrument has one 
point attached to a spring, which is regulated by a 
screw, so that very slight changes in the space may be 
made with ease. 

Compasses specially used for putting in fine circles 
and dimensions are called " bows." When a pen point 
it is a " bow pen," with a pencil point a " bow pencil," 
and if with needle point a " bow dividers." Fig. 180 
is a " bow dividers ", this fitted with screw for fine ad- 
justment in one leg, fig. 181, is called a "hair-spring 
bow dividers "; for small details, bows with steel spring 



legs without any joint are used; these are called "steel- 
spring bows." 




Fig. 185. 



Fig. 186. 



Fig. 187. 



124 



Hawkins' Mechanical Drawing. 



SPRING BOWS. 

These were originally developed from the common 
form of compasses, with a single spring leg ; later, the 
demand for smaller sizes made changes necessary, and 
spring bows are now made symmetrical, both sides of 
the bow being made to " spring." 

Fig. 182 are spring dividers. 

Fig. 183 is a spring pencil. 

Fig. 184 is a spring pen. 

In these figures it will be seen that the two 
threads, a right and a left, are moved with one central 
thumbscrew; in the figs. 185 to 187 a single screw is 
used. 

In choosing spring bows, care must be exercised 
to select a sufficiently strong, stiff spring, as the relation 
between spring pressure and thumbscrew is important. 

BEAM COMPASSES AND TRAMMELS. 

In fig. 188 is shown a set of beam compasses, 
together with a portion of the wooden rod or beam 
on which they are used. 



The latter, as will be seen by the section drawn 
to one side. A, is in the shape of a T. This form has 
considerable strength and rigidity. Beam compasses 
are provided with extra points for pencil or ink work, 
as shown. 

While the general adjustment is effected by means 
of the clamp against the wood, minute variations are 
made by the screw, £, shifting one of the points, as 
shown in the figure. 




Fig. 18S. 



Hawkins' Mechanical Drawing. 



125 




Fig. 189. 



This instrument is quite delicate, and, when in 
good order, is very accurate. It should be used only 
for fine work on paper, and never for scribing on 
metal. 

A coarser instrument, and one especially designed 
for use upon metal, is shown in fig. 189, and is called a 
trammel. There are various forms of this instrument, 
all being the same in principle. The engraving shows 
a form in common use. A heavier stick is used with 
it than with the beam compasses, and no other adjust- 
ment is provided than that which is afforded by clamp- 
ing against the stick. 

In the illustration, a carrier at the side is shown, 
in which a pencil may be placed. Some trammels are 
arranged in such a manner, that either of the points 
may be detached and a pencil substituted. 

A trammel, by careful arrangement, can be made 
to describe very accurate curves, and hence can be 
used in place of the beam compasses in many instances. 
For all coarse work it is to be preferred to beam com- 



126 



Hawkins' Mechanical Drawing. 



passes. It is useful for all short sweeps upon sheets of 
metal, but for curves of a very long radius a strip of 
sheet iron or a piece of wire will be found of a more 
practical service than even this tool. 

The length of rods for both beam compasses and 
tramels, up to certain limits, is determined by the 
nature of the work to be done. The extreme length 
is determined by the strength and rigidity of the rod 
itself. It is usually convenient to have two rods for 
each instrument, one about ij^ or 2 feet in length and 
the other considerably longer — as long as the strength 
ot the material will admit. 

DRAWING SCALES. 

Scales are proportioned rules or mathematical in- 
struments of wood, metal, etc., on which are marked 
lines and figures for the purpose of measuring sizes and 
distances. It is usual to make scales in the proportion 
of parts of an inch equalling a foot ; the most generally 
adopted scale for machine drawing is one and a half 



inches, equalling one foot ; that is, twelve-eighths of an 
inch (each eighth of an inch representing one inch) ; 
there is no fixed rule in the choice of a scale, as they 
are varied according to the coarseness or fineness of the 
parts of the machine to be drawn and the space or sur- 
face of paper to be utilized. 

When objects are of moderate proportions they 
may be represented full size ; but when large, the 
drawings must be smaller. Standard scales for me- 
chanical drawings are i, J, ^ and ^ full size. These 
scales are often written 6"=i ft. ; 3"=! ft. ; ii"=i ft., 
and I — I ft. 

Instead of selecting one of the scales named or one 
found upon the ordinary scales used by draughtsmen, 
drawings may be made to any scale whatever. Thus, 
if any object is to be represented in a certain space, a 
scale should be constructed which will cause the whole 
of the object to be shown. 

Drawing to Scale. — The meaning of this is, that 
the drawing when done bears a definite proportion to 



Hawkins^ Mechanical Drawing. 



127 



_^ • 



^ 



'^ 



Fig. 190. 



Fig. 191. 



the full size of the particular part, or, in other words, 
is precisely the same as it would appear if viewed 
through a diminishing glass. 

The two-foot rule shown in fig. 192 is the most 
useful instrument for the comparison of linear dimen- 
sions — it can be used as a scale of one-twelfth, or i 
inch equal to a foot, 12 inches = 12 feet, it being di- 
vided into portions or spaces, each of which is sub- 
divided into halves, quarters, eighths and sixteenths ; 
frequently in the latter class of two-foot rules there are 
graduations of scales, and it is then also called a 
draughting scale. 

Fig. 190 represents a flat scale, graded so that one 
inch represents a foot — xV^^ ^^^^ — ^^^•' ^^ shown. 

Fig. 191 represents a triangular scale (broken). 
The triangular scale should read on its different edges 
as follows: Three inches and i^" to one foot, i" and 
^" to one foot, J" and f " to one foot, ^" and ^" to one 
foot, j\" and -^^" to one foot, and one edge read six- 
teenths the whole 12" of its length. 



128 



Hawkins' Mechanical Drawing, 




Fig. 192. 

Fig. 190 shows such a scale broken. An explana- 
tion of the l" and i" side will suffice for all. Where 
it is used as a scale of i" to one foot, each large space, 
as from o to 12 or o to i, represents a foot, and is a 
foot at that scale. There being 12" in one foot, the 
twelve long divisions at the left represent inches ; each 
inch is divided into two equal parts, so from o to one 
division at the left of 9 is 9^" and so on. The i" and 
i" scales being at opposite ends of the same edge, it 
is obvious that one foot on the l" scale is equal to two 
feet on the -J" scale, and conversely, one foot on the ^" 
.scale is equal to six inches on the 1" scale; and 1" 
being equal to one foot, the total feet in length of scale 
will be 12 ; at i" to I foot the total feet will be 24. 



In working to regular scales, such as ^, ^, or ^ 
size, a good plan is to use a common rule, instead of a 
graduated scale. There is nothing more convenient for 
a mechanical draughtsman than to be able to readily 
resolve dimensions into various scales, and the use of a 
common rule for fractional scales trains the mind, so 
that computations come naturally, and after a time 
almost without effort. 

The protractor shown in fig. 193 is an instrument 
for laying down and measuring angles on paper ; it is 




"Fig. 193- 



Sawkins* Mechanical Drawing. 



12<) 



used in connecting with a scale to define the inclina- 
tion of one line to another. 

Protractors have the degrees of a half circle 
marked upon them ; as the whole circle contains 360 
degrees, half of it will contain 180, one-quarter 90, etc. 
Hence, protractors showing 180° exhibit all that is 
needed. To protract means to extend, so this instru- 
ment is also useful in " extending " the lines of inclina- 
tion at the circle. 

DRAWINQ=PENS. 

A special pen called a drawing-pen, and also special 
ink, are required to ink a drawing; figs. 194 and 195 rep- 
resent two sizes of drawing-pens — one being best adapted 
for fine work, and the other for coarse or heavy line 
work. The points, as will be observed in the illustra- 

Kg. 194. 

Fig. 195. ^-^^ 



tion, are made of two steel blades which open and close 
as required for thickness of lines by a regulating screw. 

A good drawing pen should be made of properly 
tempered steel, neither too soft nor hardened to brit- 
tleness. The nibs should be accurately set, both of 
the same length, and both equally firm when in contact 
with the drawing paper. The points should be so 
shaped that they are fine enough to admit of absolute 
control of the contact of the pen in starting and ending 
lines, but otherwise as broad and rounded as possible, 
in order to hold a convenient quantity of ink without 
dropping it. The lower (under) blade should be suf- 
ficiently firm to prevent the closing of the blades of the 
pen, when using the pen against a straightedge. 

The spring of the pen, which separates the two 
blades, should be strong enough to hold the upper 




IJO 



Hawkins' Mechanical Drawing. 




Fig. 196. 

blade in its position, but not so strong that it would 
interfere with easy adjustment by the thumbscrew. 
The thread of the thumbscrew must be deeply and 
evenly cut so as not to strip. 

An important requisite after the pencil lines have 
been put in is ink, with which to line the drawing. 
This should be of the best that can be procured. The 
pen is filled by dropping the ink between the blades, or 
nibs, while held in a nearly vertical position, as shown 
in fig. 196. 

Liquid India ink can be procured in bottles with 
glass tube feeders, which are very good, and keep the 



hands and fingers free of 
the ink. Fig. 197 is a sec- 
tional view of such a bottle 
and " filler," or feeder. This 
generally answers all re- 
quirements, but the dry ink 
of good quality, in sticks or 
bars, cannot be surpassed, 
although it requires skill for 
its preparation. Fig. 198 
represents a sloping dish or 
"tile" for mixing, which 
should be done with little 
pressure, in clean, filtered or 
distilled water, care being taken to keep the liquid free 
of dust, which obstructs the free flow of the ink in 
the pens. 

The bars of India ink are shown, as they are im- 
ported, in figs. 199 to 202. 

Pure India or China ink is only made in those 




Fig. 197. 



Hawkins' Mechanical Drawing. 



131 




Fig- 199- Fig- 200. 




Fig. 201. 



Fig. 202. 



countries, because the special wood from which it is 
prepared is found only in those regions. So-called 
India inks, made of lampblack and animal glue, are 
only imitations; therefore India ink should be pur- 
chased from a reliable importing house — shape is little 
guarantee of quality. 



132 



Hawkins' Mechanical Drawing. 



Soft gray vulcanized rubber (fig. 203) should be 
used for cleaning drawing paper; for erasing any por- 
tion of a line in pencil, a piece of prepared white vul- 
canized rubber is the best, small in size and of rectan- 
gular shape (see fig. 205). 

An ink eraser is made of a composition of rubber 
and ground glass, and it should be used as sparingly as 
possible on drawings, as it roughens the paper and re- 
moves the gloss from its surface (see fig. 204). Steel 
ink erasers are useful in removing defects, overrun 
lines, joint of lines if swollen, etc. ; they have a fine 
point and can be used to advantage with a little prac- 
tice; they are used with a scratching, not a cutting, 
motion (see figs. 206, 207). 

DRAWING PAPER. 

The first thing to be considered in selecting draw- 
ing paper is the kind most suitable for the proposed 
plan. Paper may be purchased in sheets 22 x 30 
inches, that make four exercise sheets iix 15 inches; 
this may be of several grades and tints. 




■'■~ -■*• -' 







I 



Fig. 204. 




Fig. 203. 




Fig. 205. 



u 



Fig. 206. 



Fig. 207. 



Hawkins' Mechanical Drawing. 



^53 



The qualities that constitute good paper are 
stren^h, uniformity of thickness and surface, neither 
repelling nor absorbing liquids, admitting of considerable 
erasing without destroying the surface, not becoming 
brittle nor discolored by reasonable exposure or age, 
and not buckling when stretched, or when ink or color 
is applied. 

The sizes and names of paper made in sheets is 
as follows: 

Cap 13x17 ins. 

Demy 1 5x20 

Medium 1 7x22 

Royal 19x24 

Super Royal ... 19x27 

Imperial 22x30 

Atlas 26x34 

Double Elephant 27x40 

Antiquarian 30x53 

For large drawings paper is made in rolls. " De- 
tail paper " is especially made for marking out new 
designs ; it is made in rolls 36, 42 and 54 inches wide ; 



it has excellent erasing qualities and takes ink and 
color with facility. 

When working by artificial light it is desirable that 
the paper be of a light-brown color, which is less trying 
to the eyes than a pure white. 

If it is a shop drawing or sketch not to be pre- 
served, use detail paper, which is the most economical 
and will stand a great deal of handling without becom 
ing soiled. If it is a detailed plan, finished drawing 
or a picture, use the best white drawing paper to be 
obtained, so that your drawings can be preserved 
indefinitely without danger of fading, which is due 
either to the paper being poorly made and discoloring 
with age, or being of poor fiber and absorbing the ink 
or color, and the drawing consequently losing its 
brightness. 

After deciding on the size of paper most suit- 
able for the work, then carefully select the paper 
embracing the most qualities of value for the proposed 
drawing. 



134 



Hawkins' Mechanical Drawing. 




Fig. 208. 





^^^H 




MECHANICAL 
DRAWING 


^ 



136 



Hawkins' Mechanical Drawing. 




Pig. 209. 



T^eebanieal ^rawing. 



In distinction to " free-hand," mechanical drawing 
is executed almost entirely by the use of the instru- 
ments previously described ; hence its other term, 
instrumental drawing. To define it particularly it may 
be said that, — 

Mechanical drawing is the correct reproduction of 
any figure or part of a machine, whether of full size or 
reduced in the proportion of one part to another ; it 
also comprises the art of delineating the interior parts 
which are hidden from view in solid bodies. 

A mechanical drawing is the vehicle for conveying 
the ideas of the designer to those who are to embody 
them in wood and metal, and the considerations which 
should govern its production are those which affect its 
clearness and legibility or those which facilitate ref- 
erence to it. 



Drawings consist of plans, elevations and sections; 
plans being views on the top of the object in a 
horizontal plane; elevations, views on the sides of the 
object in vertical planes ; and sections, views taken on 
bisecting planes, at any angle through an object. 

Drawings in true elevation or in section are based 
upon flat planes, and given dimensions parallel to the 
planes in which the views are taken. 

Two elevations taken at right angles to each other 
fix all points, and give all dimensions of parts that have 
their axis parallel to the planes on which the views are 
taken ; but when a machine is complex, or when several 
parts lie in the same plane, three and sometimes four 
views are required to display all the parts in a compre- 
hensive manner. 

A man must have either a natural talent for hand- 



i.'i? 



138 



Hawkins' Mechanical Drawing. 



drawing or years of experience, before he can produce 
a sketch and " dimension " it, fit to work from ; hence 
the elementary character of the examples given for 
practice. A "pretty" drawing is not expected from 
a beginner ; it should always be borne in mind, that 
correctness of dimensions and general clearness, rather 
than elaborate finish, are what will save the battle in 
the days of competition. 

Mechanical drawings should be made with refer- 
ence to all the processes that are required in the con- 
struction of the work, and the drawings should be 
responsible, not only for dimensions, but for adaptation 
to fitting, forging, pattern-making, moulding, and so on. 

Every part laid down should have something to 
govern it that maybe termed a "base" — some position 
which, if understood, will suggest size, shape and rela- 
tion to other parts. Searching after a base for each 
and every part and detail, the draughtsman should pro- 
ceed upon a regular system, continually maintaining a 
test of what is done. 



A mechanical drawing consists chiefly of three 
views : 

I. The plan or top view. 
2. The side elevation. 

3. The end elevation. 

In addition to the above, drawings are used to 
show interior portions of the figure; these are termed 
" sections," and they may be taken where any plane 
crosses another. 

Note. — The word elevation, as applied to mechanical draw- 
ings, means simply a view ; hence a side elevation is a side view, 
or an end elevation is an end view. 

The word plan is employed in place of the word top ; hence 
a plan view is a top view or a view looking down upon the top of 
the piece. 

A general view means a view showing the machine put to- 
gether or assembled, while a detail drawing is one containing a 
detail, as a part of the machine or a single piece disconnected 
from the other parts of the whole machine. 




Penciling. 



Fig. 211. 



It is very nearly true, as has been said, that every mechanical drawing is, in the first instance, 
penciled; if this is so, then more work is done with the pencil than with the pen; therefore the 
first attention of the student of mechanical drawing should be directed to the following instructions 
for penciling a drawing. 

With all necessary materials in hand, and in good order for the beginning of a drawing, the 
first thing to do is to pin the paper on the board quite square. 

To do this effectively, lay the paper flat and put on the T-square with its head at the left 
side of the board ; slide the square up nearly to the top, and arrange the paper level with the 
blade ; with the right hand hold the paper still and move the square down a little ; now, pin the 
top of the paper with thumb-tacks. 

139 



140 



Hawkins' Mechanical Drawing. 



Next, pressing the square lightly to the paper, 
slide it down to the bottom and pin that part of the 
paper to the board. The paper must not project out- 
side or over the edges of the board, and the pins or 
tack-heads should be forced down flush with the paper, 
so as not to interfere with the free movement of the 
tee-square up and down the board as occasion may 
require. 

The accuracy of the work depending upon their 
condition, it is first needful to see that the pencil and 
pencil compasses are properly sharpened. Reference 
is made to valuable directions contained on pages be- 
ginning with 55, under the heading of "Free-hand 
Drawing," to which may be added that — 

All lines should be drawn with the pencil slightly 
inclined in the direction in which it is moved. 

Any and all lines not needed in the finished draw- 
ing should be erased at one time after the final lines 



have been determined, for the surface of the paper is 
soiled very quickly when worked upon after erasures 
have been made. 

The working lines and other lines that are to be 
removed should be erased when the drawing is ready 
to finish and before its outlines have been strengthened, 
in order that the final lines may be left in perfect 
condition. 

To show where the lines meet or terminate it is 
needful that all pencil lines pass the actual ending 
place, making a distinct intersection. This does not 
apply to "inking in" the lines, but rather to prevent 
the over-drawing of the ink lines, because the edge of 
the rule and the pen itself obstruct or partly cover the 
view of the line, it is very liable to pass over or be- 
yond the required point in inking the lines, which must 
not occur. 



Hawkins' Mechanical Drawing. 



141 



In the preliminary operation of producing a regu- 
lar mechanical or instrumental drawing, it is necessary 
to make a " sketch," in pencil, of the object to be 
represented. The AMERICAN Machinist has given in 
a few words the order to be followed, in effecting the 
best results ; we quote, as follows : 

" In making a free-hand sketch of an object from 
the model it is well to observe the following order: 
Look the model over carefully and determine the 
number of views necessary to illustrate it fully, drawing 
the same, free-hand, in their proper relation to each 
other, on sketching paper. Look the sketch over 
carefully to see that nothing has been omitted, and put 
on dimension lines, after which scale the model care- 
fully and put on dimensions. Do not put in the 
dimensions at the same time the dimension lines are 
drawn ; have all the dimension lines in place before 
attempting to insert dimensions. 

" Follow the same order in making the drawing 
with instruments as was used in making the sketch ; 



that is, draw the views in their proper relation to each 
other, put in dimension lines, then dimensions, and 
lastly notes and title. If section drawing is made, do 
not draw section lines in pencil." 

POINTS TO BE OBSERVED IN SKETCHING. 

1. Especial attention is to be paid to outlines — 
edges of plane surfaces are lines ; when a line is made 
it represents the edge or outside of something. 

2. Learn to be accurate before being rapid. 

3. A sketch should be intelligible to any one, 
even if they are unacquainted with drawing. 

4. Horizontal and vertical lines and a few curves 
will enable one to make almost any simple sketch. 

5. It must be also remembered in making draw- 
ings from actual measurement that the instruments are 
not in the first place employed ; the rough sketch is 
first made and then it is converted into a drawing. 
The draughtsman makes a rough sketch entirely by 
the hand and eye, measures the various parts, and jots 



142 



Hawkins* Mechanical Drawing, 



down the measurements in his sketch ; after this he 
reduces the whole to the desired scale, and proceeds to 
make his mechanical drawing. 

6. Let the sketch book be the constant com- 
panion of the student ; it may be advantageously 
filled with outlines of machine or other work suitable 
for preservation, to be made into finished drawings, or 
for reference. Sketches are often valuable for reference 
as aids in originating new designs. 

7. A sketch, when possible, should have all the 
dimensions written upon it, but — 

8. Sketches in shop practice should not take the 
place of working-drawings ; the latter have a check 
upon them in being drawn to a scale — hence the 
figures written upon them and dimensions by scale 
must agree. 

9. Place title and date on each sketch — no matter 
how seemingly unimportant — for future reference. 

10. Practice sketching at every favorable oppor- 
tunity. There is no necessity for detail at first — 
simply the outlines of the article and its parts. 



II. Sketch-books, with paper bound in cloth 
covers, are utilized for bold, oiif-hand sketches by 
experienced draughtsmen, but a single sheet of paper, 
used on both sides, is not unworthy of service in an 
emergency — or even the blank side of a letter may be 
available. Sketching-blocks, or paper " pads," 4x6, or 
more, in size, and containing 48 sheets, are sold by 
stationers, and are found to be most convenient to 
have in hand and for practical use. Portfolio- 
envelopes, made of extra length paper (manila) are 
useful in filing away sketches and drawings. The size 
io>^ X 15 is used for United States Patent Office 
drawings. 

The function of the pencil — in mechanical drawing 
— is to make a path for the pen to follow. If it were 
possible to make a drawing with all its lines ending at 
the proper place, at the first time, there would be no 
necessity for using the pencil. One is obliged, how- 
ever, so to use the pencil that all lines pass beyond the 
actual ending place, thus making a distinct point for 
the drawing pen to stop at. 



Hawkins' Mechanical Drawing. 



143 



The pencil should be pressed to the paper just 
enough to make a clean, fine line, and no more ; once 
over the path is sufficient, if the line is visible and true. 

To sharpen drawing pencils, i, use a fine file, after 
taking off enough of the wood with a knife ; 2, make a 
conical point for the free-hand drawing pencils and a 
chisel point for ruling and markng distances. 

Pencil compasses are instruments where one leg is 
provided with a pencil point. Fig. 209 shows the mode 
of manipulation of those shown in fig. 180 and fig. 181. 

The pencil compass is held by the projection 
above the joint between the thumb and first finger, 
which enables it to be rotated by a movement of the 
finger without causing any undue pressure on the points. 
Should much pressure be applied, there is a tendency 
to force the point or center through the paper, making 
an ugly center mark ; at the same time the pressure 
tends to break off the pencil point. 

These few illustrations from fig. 212 to fig. 219 are 
made designedly simple, so that they may be utilized 



in " free-hand " work, for which they are good prac- 
tice, as well as serving for examples in mechanical 
drawing. 






Figs. 212. 

Figs. 212, showing a spool or bobbin, exhibit three 
views, viz. : front elevation or plan, and section ; both 
are drawn with simple lines, the end elevation by 
circles. 



144 



Hawkins' Mechanical Drawing. 





Fig. 213. 



Fig. 214. 



Figs. 213 and 214 are two side views of a hexagon 
head bolt. Figs. 216 and 217 are a square head bolt — 
two side views and end view. Figs. 218 and 219 are 
a front and edge view of a forked or double joint. 



Figs. 215 show three views of a file handle; 
the front view and section are practice for compound 
curves and curved lines meeting straight ones ; all 
these are capable of being produced by instruments. 

Moreover, many of the views and illustrations used 
to instruct and explain machine tools and other devices 
in other parts of the volume, are drawn so that they 
may be used also as examples in advanced instrumental 
practice. This is a " hint " to the diligent and pains- 
taking student worthy of remembering. 




\-/ 





Figs. 215. 



Hawkins' Mechanical Drawing, 



145 






Fig. 218. 



Fig. 219. 



146 



Hawkins' Mechanical Drawing, 



The designing and drawing of arcs and whole cir- 
cles occupy a large proportion of space in nearly all 
mechanical drawings. The making of a complete cir- 
cle is a matter of no great difficulty, but the beginning 
and termination of parts of circles require both judg- 
ment and considerable practice. 

To aid the student these two illustrations of cir- 
cles are introduced. To draw fig. 220 with a pencil, 
using the upper edge of the blade of the T-square 
as a guide, draw a center line, A B, mark on it a dis- 
tance of 4 inches, space this into half inches, using the 
dividers and making the points with it ; then with the 
pencil compasses or bow pencil, which must be held as 
shown on page 209, and rotated from left to right, or 
clockwise, draw a series of circles through these points, 
tangent to one another or all touching at A, care being 
taken that the pencil lines exactly meet at A, and 
•also cut the divided points as shown in the illustration. 
For fig. 221 divide the center line as before, and draw 
the semi-circles on it A B, B C, meeting at B, and 
6'Z>, Z>^, etc. 



Fig. 220. 



Fig. 221. 




Hawkins' Mechanical Drawing, 



147 



Now from center B draw circles A C, C E, meet- 
ing in G, and so on with the circles, arcs or segments ; 
success in drawing this figure depends on the correct 
spacing of the center line in the first instance into 
equal parts. 

The T-square should be used for drawing horizon- 
tal lines only. Its head should always be placed upon 
the left edge of the board. Vertical lines should be 
drawn by the use of a triangle placed upon the T- 
square and not by means of the T-square only ; because 
the edges of a board are seldom at right angles to each 
other, and the blade of the T-square is often not at 
right angles to the head, so that lines at right angles to 
each other will not result from the use of the T-square 



upon all edges of the board. Only the upper edge of 
the T-square should be used, as the edges are often not 
quite straight or parallel. 

The 45° triangle has two angles of 45° and one of 
90°. The 30° and 60° triangle has an angle of 30°, one 
of 60°, and one of 90°. By placing these triangles upon 
the T-square, lines at any of these angles with a verti- 
cal or horizontal line may be drawn. 

Drawings finished in ink are much more effective 
and desirable than pencil drawings ; but as a good inked 
drawing cannot be made except upon an accurate pen- 
cil drawing, students should begin with the pencil, and 
should not use ink until they are able to produce satis- 
factory results in pencil. 



Ppojeetion. 



The word projection means to throw forward, and in ordinary machine drawing it is the projecting or 
throwing forward of one view from another view. 

In drawings the lines in one view or plan may be availed of to find those of others of the same object, 
and also to find their shape or curvature as they would appear in the other representations ; this is called 
projection-drawing. 



Fig. 222 is the illustration as shown in fig. 212 on 
page 143, with the addition of dotted projection line, 
which illustrates the method of throwing forward the 
section and the end view of the object ; these two 
views are procured from the plan or first figure, as 
shown in fig. 222. 

Fig. 224 represents the square bolt and nut shown 



in fig. 216, and the mode of projecting is similarly 
shown by dotted lines. 

Fig. 223 shows file handle shown in fig. 215 and 
the mode of projecting. 

The principles upon which " projection '* in draw- 
ing is based, are illustrated in the following examples 



14S 



Hawkins' Mechanical Drawing. 



149 




Fig. 222. 




Fig. 224. 




Fig. 223. 



and text : As a real object can be scaled with a foot 
rule, so a drawing must permit of scaling and measur- 
ing. This measuring may take place as with the real 
object in full size or the drawing may, for the sake of 
convenience, be reproduced and measured in a reduced 
scale, as half, or in still smaller sizes. Sometimes it 



I50 



Hawkins' Mechanical Drawing. 



may prove convenient to enlarge the drawing to twice 
the natural size of the object, as a means of making it 
stand out more clearly than the real size would 
accomplish. 



For practical purposes, it is productive of economy 
of time to mark the dimensions of height and width 
or depth on the drawing in figures, to avoid the scal- 
ing. This marking of the dimensions is best done at the 
time of making the drawing, while the conception of 
the object is clear. 

To convey a correct impression of the object, all 
lines that are marked to be of equal length should appear 
equally long on the drawing and be capable of being 
scaled to such equal length ; for this, it must be as- 
sumed that the eye of the observer is equally distant 
from all points of a plane through the nearest point, or 
one of the axes of the object, and that the lines 



of sight are all parallel to each other and square to 
this plane. 

In fig. 225 these lines of sight are seen as directed 
toward one side of a cube or block ; it will be readily 
understood, however, that in this way nothing is vis- 
ible and accessible for scaling and dimensioning except 
this front face of the block, thus, a determination of 
the dimensions of only height and width would be pos- 
sible, while the dimension of depth is entirely unde- 
termined. 

It is thus necessary to get a view of the block from 
another side ; the direction in which it will be most 
instructive to obtain additional views is in the direction 
of the breadth and of the length and square to the 
lines of sight of the first view. 

Fig. 226 shows how the lines of sight would strike 
the object in the three directions. If these lines should 
be rays of light, some of them would pa.ss by the body 



Hawkins' Mechanical Drawing, 



151 




iqHT Lines 



Pig. 225. 



until they squarely strike the large plane surfaces, 
/, //, ///; naturally the rays of light on the faces of 
the object will be retained, and cannot strike the plane 
surfaces, thus leaving dark shadows of exactly the same 
outlines as the block ; these would be exact drawings, 
of the faces, and if by some means they can be fixed 
and retained on the plane they can be completely 
measured and dimensioned. 

This throwing forward of the outline of the object 
in different views on the planes is called projection of 
the object, and furnishes a highly important means of 
fixing the outlines and dimensions in the three main 
directions of height, width and depth ; evidently, the 
light rays passing by the front face may not all reach 
the plane of projection, but they may be retained by 
protruding parts of the object behind the front face. 
These protruding parts naturally would also be pro- 
jected on the plane in the same manner as the main 
body of the block. 



^52 



Hawkins' Mechanical Drawing. 



These projections of the protruding part are plainly 
visible in plane // and plane ///, while the part would 
not be drawn in outline in plane /. It may be imag- 
ined, however, that the greater thickness of the body 
in the direction of the protruding part would intensify 
also the shadow, thus outlining the face of the protrud- 
ing part in plane /. 

It is apparent that these three projections are all 
needed, but as drawing is all done in one single plane, 
the three projections will for the sake of convenience 
have to be brought into a single plane. This can be 
realized if plane // is swung around axis O Z and 
plane /// around axis O V, until all three surfaces are 
in one single plane, which would then appear as shown 
in fig. 227. 

It is also possible to assume transparent planes in 
front of the body and extend the parallel lines of sight 
forward instead of backward. Thus an outline picture 
will be created on each of the three planes /, //, /// in 
fig, 228. in a manner similar to fig, 226. For drawing 



purposes, all three views again have to be brought into 
a single plane, which is done by swinging // around 
(9 Z, and ///around O Y in the same manner as fig. 227 
was evolved from fig. 226. 

It will be noted that in fig. 229 plane /// is now 
above / and plane // on the left-hand side of /, while 
in fig. 227 they were below and at the right-hand side 
of plane /. As the swinging of the top and side planes 
takes place around the edges of the front plane / two 
systems may thus be distinguished, according to the 
position of plane / in regard to the object. Fig. 226 
thus represents the system of backward projection, 
while fig. 228 represents the system of forward pro- 
jection. 

Either system can have, however, the plane // at 
the right- or left-hand side edge, while plane /// may 
be attached to the top or bottom edge of plane /; it 
is readily understood that a number of combinations 
are possible for each system, as it is not necessary to 
adhere absolutely to one rule. The system of forward 



Hawkins' Mechanical Drawing. 



153 




154 



Hawkins' Mechanical Drawing. 




ih 



I. 




% 



K 




^^^ 



T 



Fig. 227. 



Hawkins' Mechanical Drawing. 




155 



156 



Hawkins' Mechanical Drawing. 



projection is the one g^enerally practiced and further 
examples are all executed by this system, meaning that 
the planes are always between the observer and the obj ect. 

For the clearness of the drawing, it is desirable to 
have all corners, edges and outlines appear in such 
solid lines as they appear to the eye. If, therefore, 
certain sharply defined outlines occur on one side more 
than on the opposite one, it is most desirable to take the 
view against the side that has the most definitely 
marked outlines. 

If the opposite side should show a number of 
wholly different features, it may prove even desirable 
to show this side also, thus gaining four views instead 
of the usual three, and so obtain a more complete 
understanding of the shape of the object, besides 
giving increased facilities for dimensioning each part of 
the body. 

This additional view may be taken from the sides, 
as well as up or down, thus making a maximum of five 



views possible by which the outside of the object may 
be delineated. 

Fig. 230 shows why it may be desirable to take 
five views of a block that has a receding space of dif- 
ferent outlines in each of the side and top and bottom 
faces. 

It is not necesssary, however, to resort to five 
views in such a case as is represented in fig. 230, as the 
only differing feature, the circular space in /// bottom, 
might be shown in /// top by dotted lines, and the 
difference of // right might be shown in // left, also by 
dotted lines. It is desirable to show four or five views 
only where great complication and consequent lack of 
clearness through numerous dotted lines would result 
from having a less number of views. 

So far the projections and views have only repre- 
sented the outlines of the object ; it may often be 
desirable, however, to show central holes or other per- 



Sawkins' Mechanical Drawing. 



157 



forations or variations of sections ; in this case it is 
possible to imagine the object cut in slices, by planes, 
through certain well defined axes, or other lines of 
distinctive importance, and then take a view of this 



.XI 




Fig. 229. 



158 



Hawkins' Mechanical Drawing. 





1-ToP 
















- \ 










F-Leh. 




I 


! 
! 

i 




X~ RIQMT 






m 






U i 

y [ 

r— . 






p-» 




















Jt-BOTT. 















Fig. 230. 













Hawkins' Mechanical Drawing. 



159 



sectional plane mth its newly created intersections or 
sharply marked outlines; thus, a section may often 
lake the place of the third, fourth or fifth view to great 
advantage. 



It is not always possible to get a view against a 
face or side of the object, but, with irregularly shaped 
bodies or under special conditions, it may be neces- 
sarj' to take a view of comers, sloping planes, curved 
or irregularly shaped surfaces. 



and these are therefore the right places for scaling and 
dimensioning in the vertical direction. 

Fig. 231 shows how a cylindrical outline appears 
in the three views ; the hole in the nut presents itself 
as circular in the top view, while it appears in the front 
and side views as a rectangle. For simple objects,' rt 
is unnecessary to show the edges of the planes, and the 
three views are grouped, as regards distances and posi- 
tions, as most convenient for the execution of the 
drawing. 



Fig. 231 shows a hexagonal nut in the three nor- 
mal projections ; from the top %'iew it is readily seen 
that the front view shows the side of the hexasfon in a 
contracted scale, and that therefore the scaling and 
dimensioning for the horizontal direction have all to be 
done in the top or plan view ; the front and side views 
convey, however, the dimension of height correctly, 



Where sloping surfaces are of irregular form, it 
may be necessary to employ help lines for their full de- 
termination in the three views. Fig. 232 shows how 
the surface that is produced by a slanting cut through 
a cyUnder would appear in the three views. The help 
lines are placed in the top view in eight equal divisions 
around the circumference of the cylinder. These divi- 
sion lines are shown by dotted lines on the cylinder in 



i6o 



Hawkins' Mechanical Drawing 



the front and side views. Their intersections, with the 
sloping cut in the front view, furnish also the height 
of the corresponding points for the side view. 

By progressive determination of points, lines and 
surfaces, even the most complicated bodies can be 
completely represented for their reproduction in any 
application to mechanical or industrial purposes. 



DC 




a b 

Fig. 231. 



A^ 



f 



Hawkins' Mechanical Drawin g. 



i6i 




l62 



Hawkins' Mechanical Drawing. 



The spur wheel shown on page 163 is an example 
of projection drawing. 

The wheel is illustrated in three views: fig. 235 is 
a side view, or elevation ; fig. 234 is a front elevation ; 
fig. 233 is a section view on CD. The section is pro- 
jected from the front elevation by drawing parallel 
lines from the points in front elevation where the lines 
are intersected by the center line CD, cutting the 
plane of view and showing the interior shape at CD. 

The side elevation, fig. 235, is projected from the 
front elevation, fig. 234, by drawing parallel lines 
from the edges in the front view across its face. 

In actual drawing practice the figures should be 
made about three times larger than the example, and 
as follows : 

For the front elevation draw the center lines ^ B, 
C D, and from their point of intersection as a center, 
with the compasses draw the inner circle or hole, also 
the pitch line ]£ E. With the dividers space this line 



into nineteen equal divisions ; each point on this line 
will be the center of a tooth, and the distance from one 
point to the next one is the pitch of the tooth. 

Now, with the dividers mark off the thickness of 
tooth at each side of these points on pitch line ; with 
the compasses draw the outer circle for points of teeth, 
the inner circle for the root of teeth, and circles for 
thickness of rim and hub ; also circles representing the 
fillets at rim and hub. For clearness and to prevent 
confusion these lines are shown on one-half the wheel 
only, terminating in center line C D\ all the lines of 
the front elevation are now complete excepting the 
teeth. 

In the drawing ofifice it is unusual to delineate all 
the teeth in a gear wheel, the lines without the teeth 
as now completed being deemed sufificient, giving all 
particulars ; however, to prevent the error of mistaking 
the circles it is well to represent one or two teeth on 
the drawing. 

In the example, proceed and complete the entire 



Hawkins' Mechanical Drawing. 



163 




A 



B 



Fig- 233 



Fig- 235. 



164 



Hawkins' Mechanical Drawing. 



wheel, taking on the compasses a radius equal to the 
pitch of the tooth ; set them on the pitch line at the 
point G, already spaced for thickness of tooth, draw 
line // from pitch line to root of tooth ; proceed simi- 
larly all around the circle, completing one side. Next, 
reverse the operation and draw the corresponding side 
of the root of tooth. Now take a radius equal to half 
the space between teeth and the thickness of tooth on 
pitch line, and, with center in pitch line, as shown at 
/. draw the outside or addendum of tooth,/; it will be 
apparent that the reverse addendum of the tooth next 
adjoining can be formed at the same time, with one 
setting of the compasses ; finish all the teeth similarly; 
the front elevation will thus be completed. 

Fig. 233 is an excellent example of sectional draw- 
ing, to be executed as follows : 

First draw the center line L M oi fig. 233, lay off 



at each side of it half the breadth of face and of the 
hub; now project, from center line CD, in the front 
elevation, fig. 234, with the T-square the upper and 
lower teeth, the fillets, the chamfers, the hub and cen- 
ter hole, also dot in the pitch line F F, take the radii 
and draw the fillets and chamfers; draw section lines 
and the view will appear as shown in fig. 233. 

Fig- 235 is a side elevation of fig. 234, and is a fine 
sample of projection, to be executed as follows : 

Proceed similarly as for fig. 233, projecting the 
lines from the outside edges of the front elevation, in- 
stead of from the center line (7 Z> as in last figure, and 
the end elevation will be as shown in fig. 235. 

The student will be assisted in understanding this 
working drawing by consulting the pages under the 
heading of " Gearing." 



1 66 



Hawkins' Mechanical Drawing, 




O 




Fig. 236. 



(( 



Inlying In" J^raw^ings. 



When a drawing is completely finished in pencil- 
ing, it should next be " inked in " for preservation. 

Care should be used that the pen may be perfectly 
clean ; the pen should be held nearly vertical, leaning 
just enough to prevent it from catching on the paper ; 
the pen should be held between the thumb and first 
and second fingers, the knuckles being bent, so that it 
may be at right angles with the length of the hand. 

The ink should be rubbed up fresh whenever it is 
about to be used, for it is better to waste a little time 
in preparing ink slowly than to be at a continual 
trouble with pens, which will occur if the ink is ground 
too rapidly or on a rough surface. 

To test ink, a few lines can be drawn on the 



margin of a sheet, noting the shade, how the ink flows 
from the pen, and whether the lines are sharp. After 
the lines have dried, cross them with a wet brush ; if 
they wash readily, the ink is too soft ; if they resist the 
water for a time and then wash tardily, the ink is 
good. 

Care must be exercised not to overload the pen 
with ink, and, like the pencil, the pen should always 
be moved from left to right and from the bottom to 
the top of the board. When inking, both ' nibs " of 
the pen point must rest evenly on the paper and the 
pen be pressed only lightly against the T-square. 
Never ink any portion of a drawing until the penciling 
is complete. 



167 



i68 



Hawkins' Mechanical Drawing. 



In inking long, fine lines it is well to go over each 
line twice, without moving the T-square, trying not to 
widen the line on the second passage ; also see that 
the pen contains ink enough to finish a line, as it is 
difficult to continue with the same width of line after 
re-filling. 

To produce finished drawings, it is necessary that 
no portion should be erased, otherwise the color applied 
will be unequal in tone ; thus, when highly finished 
mechanical drawings are required, it is usual to draw 
an original and to copy it. Where sufficient time can- 
not be given to draw and copy, a very good way is to 
take the surface off the paper with fine sand-paper 
before commencing the drawing ; if this be done, the 
color will flow equally over any erasure it may be 
necessary to make afterwards. 

The rules of procedure in drawing the lines in 
"inking" are, i, ink in the small circles and curves; 
2, ink in the larger circles and curves ; 3. then all 



the horizontal lines, beginning at the top of the 
drawing and working downward ; 4, next ink in all the 
vertical lines, commencing at the left and moving back 
to the right ; 5, draw in the oblique lines ; 6, all the 
center lines and dimension and reference lines. The fig- 
uring and lettering should be always done with India 
ink, thoroughly black ; the last lines to be drawn are 
the section lines. The reason why irregular curves 
and arcs of circles are inked in first is, that it is easier 
to draw a straight line up to a curve than to take a 
curve up to a straight line. 

In practice, the flat side of the drawing-pen is laid 
against the tee-square or ruler; the taper of the blade 
of the pen is sufficient to throw the point enough away 
from the edge to prevent blotting; the pen is drawn 
from left to right and from the bottom to the top of 
the board. 

This is shown in fig. 237, intended to represent 
"short work" with the drawing-pen. The wrist is 
shown resting upon the blade of the square. 



Hawkins' Mechanical Drawing. 



169 



In a similar figure, 238, the position of the hand 
holding the pen indicates the best relative posture for 
inking long lines. In one of these illustrations the 
work is executed principally by the wrist — in the other 
by the arms and fingers working together. 

The pen should be held with even pressure against 
the straight-edge or cur\-e. If the pressure varies, the 
blades will spring and the width of the line will change. 
The blades should be of such length that both will 
bear equally upon the paper when the pen is inclined 
slightly, so as to bring the inner blade near the straight- 
edge; the angle of the pen should not be changed 
while drawing any hne. 

When the inking is finished, the whole drawing 
may be cleaned by rubbing it with bread which is not 
greasy or so fresh as to stick to the paper. If the 
paper is much soiled it may be necessary to use an 
eraser. A soft pencil eraser should be used and great 
care taken that the ink lines are not lightened and 
broken by it. 




Fig. 237. 



170 



Hawkins' Mechanical Drawing. 



To avoid the necessity of using an eraser upon a 
finished drawing, instruments and paper must be kept 
free from dust and dirt. The triangles and T-square 
should be cleaned often, by rubbing them vigorously 
upon rough, clean paper. 

Pounce is a powder used to prevent blotting in 
rewriting over erasures; it is held in a bag or small 
box with a perforated lid for convenience in sprinkling 
on paper ; when used it should be distributed evenly 
with a piece of chamois, and the surplus or loose par- 
ticles removed before applying the ink. 

A drawing is made to be read, and the skill in ink- 
ing, as in " free-hand " and in penciling, does not con- 
sist so much in the fineness of the lines as in their 
clearness. 




I^ettering j^pawings. 



Lettering is an important part of making draw- 
ings, the object aimed at being to identify any portion 
by reference letter or letters; thus in fig. 239 the line 

A describes the ^m^^^^^^^^^^^^^^^^^^ 
extending from |H^^^^^^^^^^^^^^^3^^^ 

Fig- 239- 

Any information which cannot be expressed in the 
drawing is always expressed by lettering, and it is de- 
sirable to confine the lettering of drawings to one or 
two standard alphabets that are plain and distinct, and 
the principles of which are easily acquired. These condi- 
tions are fulfilled in the Gothic fonts shown on page 173. 

Both letters and figures must be carefully made 
and of uniform proportion ; it is well to " lay out " 



these by regular measurement before permanently 
inking them. Letters should not be less than one- 
eighth of an inch in height and penciled carefully 
before inking. 

On page 173 are printed two forms of numerals and 
letters of the alphabet ; it is recommended that these 
be used both for practice in free-hand and for regular 
office work. 

For easy reference, letters should not be crowded 
nor allowed to interfere with one another ; they should 
be drawn neatly, avoiding all lines of the drawing; 
plain letters are always used on mechanical drawings, 
whether for title, scale, reference, etc. 



171 



172 



Hawkins' Mechanical Drawing. 



Arrow-heads, figures and letters should be in black, 
and made with a writing pen. A pen with a ball point 
is preferable, giving an equal thickness of line, no mat- 
ter in which direction the stroke is made. 



location, to draw, with a round-pointed pencil, two 
horizontal lines just the height the letters are to be ; 
the letters are also best made with careful use of the 
instruments, rather than free-hand. 



291; 











1"^ 


i Mas 


3 




'§1 






io> 


si 


1 i» 


70j 


303 



Fig. 



Neat, well-lettered drawings go far towards estab- 
lishing a high standing for the aspiring draughtsman. 
All lettering should be done free-hand, first with the 
pencil, sharpened to a fine round point, and afterwards 
written in ink. For this purpose common writing pens 
are best to be used ; fig. 240 represents the several 
numbers of the approved Gillott's pens adapted to this 
purpose. 

In lettering, it is well, for a guide for size and 



In order to letter systematically, it is a good plan 
to start with the middle letter of the inscription and 
work in both directions ; making too prominent letters 
should be avoided, plain and distinct letters being most 
desirable. 

Finally, with an ordinary writing pen, trace over 
the penciling in ink; the pencil guide lines being 
erased after the letters are inked in completes the 
operation. 



Hawkins' Mechanical Drawing. 



177 



Arrow-heads and figures should be drawn free-hand 
with a common writing pen. 

Usually dimensions are given in inches, up to 24 
inches, as it is found less confusing ; for instance, if 
written i' i" it may be mistaken for 11" ; if written 13" 
no mistake could be made. 

Again, 1' o" may be mistaken for 10" ; if writ- "'J'" 
ten 12" it would not; in addition to being more ' 

distinct, it occupies less space on the drawing. In ] 

large measurements there is more room for the , 

figures, and, therefore, they can be spaced ^ 

further apart — in feet and inches. ^ 

All figures should be made of a fairly 
large size. Vertical dimensions should read • 

from the right hand, thus, as shown : f 

Measurements of importance, such as " "_ ^ 
the diameter of a circle, the pitch or dis- . 

tance apart of rivets and bolts, etc., should ' 

be marked in figures on the drawing. When 
rough or unfinished work is mixed with V/ 



machined or finished portions, it is usual to mark F, 
or "fin.," after the latter dimension. 

In practice, at times, instead of dimensions refer- 
ence letters are used, thus ; 



<-- L --4 



fTi 



■TT 



D. 



^T-^ 



I 



jr 




D=diam. of shaft, 2^ inches. 

L^length of bearing, 3f inches. 

T^ — ^thickness of collar, -| inch. 

D=^diam. of collar, 3^^ inches. 
Generally it is preferable to give the diameters of 
turned and bored work on a section, instead of an end 
drawn separately •, confusion is sometimes caused by a 
number of radial dimensions. 



178 



Hawkins' Mechanical Drawing. 



Fig. 242 and fig. 243 are introduced to show the 
principal measurements required in practical work, and 
the usual way in which such dimensions are marked 
when ordering parts of machinery. 

Fig. 242 is a pedestal, or metal frame ; three views 
are shown, the center figure being an elevation, the 
lower figure is the plan of the base, the upper figure is 
a view of the top, on which is bolted the bearing block, 
it being on the outside of the center figure. The 
essential measurements are marked by letters. H is 
the vertical height from base to the seat of bearing 
block: L being the length, and W the width of the 
base ; P is the length between checks, and B the width 
of seat for bearing block ; C is the distance from center 
to center of the holding down bolt holes, and T is the 
depth of the holes in the base ; K is the distance from 
center to center of the bolt holes in the top for bearing 
block. 



Fig. 243 is a hanger, or metal bracket, and shows 
the center figure or elevation, the plan of the top and 
the plan of the seat for bearing block, which is bolted 
on the interior of the center figure. H is the vertical 
distance from the top to the seat for bearing block ; 
the other measurements required are marked by letters 
similar to figure 242. 

Now, one of the important matters in connection 
with dimensioning a drawing is the location of the fig- 
ures. One rule, whose utility cannot be gainsaid, is 
that they should be so located that they can be altered 
or erased without damage to the lines of the drawing, 
as changes may be necessitated either by original errors 
in writing down the figures or by changes in the de- 
sign being found desirable during the construction of 
the machine. 



Hawkins' Mechanical Drawing. 



179 



wm. 




K P-- '--». 



k — K--^ 




CD 

K 



— T 

I 

-- 1 

X 



I 

I 

I 

I 
I 
I 
I 
I 
I 



rm 



-X. 



L 



1^.243. 



— -L^^ 



1 
*>— ( ' 


f-— ■ — ^ 


1 




r<— K— *< 



^IL 



t 



Fig. 244, 



Shading I^rawin^s. 



To produce an effect, drawings are shaded ; that 
is, shadow lines about twice the width of the regular 
line are drawn according to a recognized rule, which 
always represents the same peculiarity of form in the 
same way. 

In working drawings light lines only are permitted ; 
shade lines are wider than the working lines, and in 
reading scale measurements the extra thickness of line 
would make a difference. 





Instead of representing the shadow as it is really 
cast by the object, the edges which cast the shadow 
are determined, and all the views are treated as if the 
light came from behind and from the left, downwards, 
at an angle of 45° to the horizontal line, as shown by 
the arrows in figs. 245 to 248. 

The lower and right-hand outlines of projecting 
parts will cast shadows, and the student should make 
them of extra width. 





Pig- 245- 



Fig. 246. 



180 



Fig. 247. 



Fig. 248. 



Hawkins' Mechanical Drawing. 



i8i 



Fig. 249 : In shading curves, divide the center line as 
before (see page 146) and describe circles from center, D ; 
these lines are not to be shaded in penciling, but when 
inking. The figures represent two rings, A and C, and 
spaces, £ and D. The outside of a surface is shaded 
according to circle i, and the inside surface according 
to circle 2. This will give the desired shading, but it 
makes a drawing incorrect, and therefore shading is not 
used in working drawings. 

This shading is accomplished by inking the circle 
first with regular width of line ; then with the same ra- 
dius remove the point of compasses from the tri^e cen- 
ter, placing it outside, according to the desired position 
of the shaded line, and describe an arc of a circle. 

In fig. 250 divide center line as before ; with the 
45° triangle or set square, draw through the center the 
diagonals shown by dotted lines ; and through the 
points A, B, C, etc., draw the perpendiculars, cutting 
the diagonals ; from the points of intersection draw the 
horizontal lines, completing the squares. 




Fig. 249. 

carefully the lines 
joining with the 
arcs ; all lines must 
be of the same 
width ; put in the 
shade on arcs and 
lines as in fig. 249 ; 
and, finally, erase 
the pencil lines at 
comers, etc. 



Now, take a ra- 
dius of half an inch, 
and in the corner of 
each square draw 
with the bow-pencil 
a circular arc meet- 
ing the pencil lines 
exactly ; with the 
bow-pen ink in the 
arcs first, then ink 




Fig. 250. 



Seetion-Ci"in^. 



Cross-hatching has been defined in the "prelimi- 
nary definitions" to drawing; this term represents the 
practice of drawing diagonal lines representing the in- 
terior of an object, shown as a piece cut in half or 
when a piece is broken away. This is done to make 
more of the parts show, or to exhibit more clearly the 
nature of the materials ; hence section lining and cross- 



hatching tell the same thing, /. e., the drawing of diag- 
onal lines, usually at an angle of 45°, to show that the 
object is broken away and the interior designed to be 
represented. 

Figs. 251 to 258, inclusive, show the section lining 
and cross-hatching by which it is customary to repre- 
sent the various materials entering into a construction. 





Cast iron. Wrought iron. 

Fig. 251. Fig. 252. 









Steel., 


Composition 




Vulcanite. 


Wood. 


Leather.. 


Brick.. 


Fig. 253- 


Fig. 254. 


182 


Fig.- 255. 


Fig. 256. 


Fig. 257. 


Fig. 258. 



Hawkins' Mechanical Drawing. 



183 




In fig. 259 is outlined a 

representation of a section of 

a cog-wheel ; section i being 

the wood cogs ; 2, the iron 

wheel, and 3 the wedges at 

the root of the gear. It would 

be impossible to convey the 

^g- 259- same ideas by ordinary plan 

oT elevation drawing; all the objects on the same page 

are more clearly represented by the use of section 

lines or cross-hatching. 

Sectioning is executed by drawing a series of par- 
allel lines about /^ inches apart. Lay the 45° triangle 
or the upper edge of the T-square and draw the top- 
most line of the sectioning. Then slide the triangle 
along the T-square for each successive line. The sec- 
tioning should be inked in without previous penciling 
and the lines should be finer than the lines of the gen- 
eral drawing. 

Various devices are in use for mechanically equal- 



izing the distances in section lining, but the trained 
eye is the most practical method. When two abutting 
pieces are sectioned, the section lining on one piece 
slants in an opposite direction to that on the other. 

To draw an object to be sectioned on both sides 
of its center line, only one side is sectioned, while the 
other side is drawn in full. 

Sections are necessary in nearly all machine draw- 
ings ; they are usually taken horizontally or vertically, 
but they may be taken in any direction ; the position 
of a section should be shown by a line upon the object ; 
this line is called the cutting plane. 

In fig. 261 is shown the hub of a wheel, it is also a 
sample of work for practice. 




Fig. 260. 



i84 



Hawkins' Mechanical Drawing, 



Fig. 260 shows the mode of representing two 
different materials in one plane, or a section may be 
represented by the darker portion, and the lighter 
shaded portion being a surface resting on the section. 

Fig. 261 shows the section of a shaft surrounded 
by the surface of a wheel. 




Fig. 261. 



TINTS AND COLORS. 

For special purposes of illustration drawings are 
made which must be tinted. In such cases the paper 
must be expanded and stretched evenly all over its 



surface ; otherwise when the moist tint is applied the 
paper will wrinkle and get out of shape; to do this 
cut the paper at least half an inch less in size than the 
drawing board ; lay the paper face down, turn up a 
margin or edge of about three-fourths of an inch all 
round, then dampen the paper with a sponge and clean 
water; allow it to soak for a few minutes, until it is 
evenly dampened or moistened all over, turn the paper 
upside down (face up). 

Apply strong paste to the under side of the margin 
all round ; rub down, on the drawing-board, working 
from the center of the board outwards so as to exclude 
the air and prevent creases or furrows. The board is 
then inclined and left to dry slowly ; make sure that the 
paper is all well pasted and every part of the edges 
attached to the board. 

If tracings are required to be tinted or shaded, 
the color may be applied before the tracing is cut oif, 
or what is more usual, the color may be applied on the 
back of the tracing ; then there is no liability to wash 
out the lines. 



Hawkins' Mechanical Drawing. 



185 



Mechanical drawings are seldom tinted, but are 
mainly produced in India ink. Where, however, a fine 
effect is desired, working drawings are colored, so as to 
show at a glance the material of which the different 
parts are to be made. 

The colors required are few but should be of the 
best quality. Besides India ink the following water- 
colors are generally used : 

I, Neutral-tint. 2, Prussian Blue. 3, Chrome 
Yellow. 4, Gamboge. 5, Raw Sienna. 6, Carmine. 
7, Vermillion. 8, Venetian Red. 9, Sepia. 10, Indigo. 
These come in hard cakes. 

Certain colors and tints represent different metals 
and materials as follows : 

Wrought Iron — Prussian Blue. 

Steel — Carmine and Prussian Blue, mixed to give 
a purple shade. 

Steel Casting — Same as the above darkened by 
Venetian Red. 



Cast-Iron — Neutral Tint made of India Ink, in- 
digo, mixed with a little carmine. 

Brass — Gamboge or Chrome Yellow. 

Babbitt — Emerald Green; sometimes light 'mix- 
ture of India Ink. 

Copper — Purple Lake. 

It is sometimes found necessary to prepare a highly 
finished and shaded drawing of the work in hand. 
Such elaborations, in fact, are much admired by the 
uninitiated, although the complete shading of the 
drawing is no criterion as to the scientific value of the 
machine. An illustration of this is told in the note. 

Note. — A consulting engineer had to lay before a board of 
directors plans of horizontal engines for their consideration. One 
of these drawings was of a very superior machine, but being only 
depicted lineally was at once rejected by them, for a highly 
finished representation of a very inferior apparatus. The engineer, 
wishing to induce the board to decide for the best, suggested that 
the matter should be postponed to a future day, and in the mean- 
time had the drawing of the superior machine highly colored and 
finished. At the next meeting the directors unanimously decided 
that this was the very one which they preferred and had chosen. 



Reproducing Qpawings. 



When once finished, one or more copies of draw- 
ings are frequently required ; these are produced, i, by 
blue printing, as described before ; 2, by tracing. A 
tracing is a mechanical copy of a design or drawing, 
made by reproducing its Hnes as seen through a trans- 
parent medium — as tracing-cloth or tracing-paper. 

Tracing-cloth is a thin linen fabric, coated with 
size ; this is called tracing-lines ; tracing-paper is so 
prepared as to be transparent, so that it will receive 
marks either in pencil or with pen and ink. 

Tracing-cloth must be fastened to the board, over 
the drawing, by pins or other tacks ; moisture or damp- 
ness should be carefully avoided and the drawing done 
on the smooth side of the cloth. 

When tracing cloth will not take ink readily a 
small quantity of pounce may be applied to the sur- 



face of the cloth and distributed evenly with a piece 
of cotton waste, chamois, or similar material, but the 
pounce should be thoroughly removed — by washing — 
before applying the ink. 

In making tracings the same order is followed as 
described under the section " Inking " — to repeat : 
I, ink in the small circles and curves; 2, ink in the 
larger circles and curves ; 3, then all the horizontal 
lines, beginning at the top of the drawing and working 
downward ; 4, next ink in all the vertical lines, com- 
mencing at the left and moving back to the right ; 
5, draw in the oblique lines ; 6, all the center lines red 
(carmine), and dimension and reference lines in blue 
(Prussian blue) or vice versa. The figuring and letter- 
ing should always be done with India ink, thoroughly 
black. 



186 



Hawkins' Mechanical Drawing. 



187 



BLUE PRINTING. 

Copies of drawings or parts representing details 
and measurements are frequently needed for the office, 
pattern shop, machine and blacksmith shop, etc. These 
copies are best made by printing on sensitized or 
specially prepared paper, from tracings drawn on trans- 
parent cloth or paper, as hereabove described. The 
original design may be guarded with the utmost care 
for long preservation, but the blue prints, so called, are 
for ready reference and use without much regard to 
the length of time they are to be in existence. 

The usual practice is to carefully trace from the 
drawing on transparent cloth or paper an exact repro- 
duction of it, filling in all detail lettering and sizes or 
figured dimensions. 

This tracing is fixed in a frame similar to a picture 
frame, with the side on which the drawing is made 
next to the glass: i, place the sensitized side of the 
paper (which has been prepared previously) against the 
back of the tracing ; 2, fix soft padding against the 



back of the paper and fasten it up so that both paper 
and tracing are compressed firmly against the glass, 
permitting no creases or air spaces between them. 

This should be done in a darkened room ; 3, ex- 
pose for three to six minutes, according to the intensity 
of the sun ; 4, take the sensitized paper out of the 




Fig. 262. 



1 88 



Hawkins' Mechanical Drawing. 



frame and quickly wash well in clean running cool 
water, and the drawing will appear in white lines on 
blue ground ; 5, hang the print up by one edge so that 
the water will run off and the print will soon dry and 
be ready for use. 

TEST=PIECES. 

To make good blueprints, being guided only by 
the appearance of the exposed edge of sensitized 
paper, requires considerable experience. Very often, 
especially on a cloudy day, the edge looks just about 
right, but when taken out of the frame and given a 
rinsing, it is only to find that the print looks pale 
because it should have been allowed to remain exposed 
for a longer period. 

Now simply take a small test-piece of the same 
paper (say about 4 inches square) and a piece of 
tracing cloth with several lines on its surface and 
lay these small pieces out at the sam.e time the real 
print is being exposed, and cover these samples 
with a piece of glass about 4 inches square. As a 
general rule, we can find a place on top of the frame 
for the testing-piece, and by having a small dish of 
water at hand for testing the print by tearing off a 



small bit and washing same to note its appearance, 
the novice can get just as good results as the experi- 
enced hand without danger of failure. 

BLACK PROCESS COPYINQ. 

This is accomplished by specially sensitized paper 
bj'^ which a fac-simile of the original drawing can be 
made ; that is, black lines upon white ground. It also 
avoids the objection to the blue print paper of shaded 
drawings which show light and shade reversed. 

The prints made by the process are said to be 
absolutely permanent and can be altered, added to or 
colored the same as original drawings. 

The sensitized paper is sold ready for use, but it 
can be prepared by dissolving two ounces of citrate of 
iron and ammonium in eight ounces of soft water ; 
keep in a dark bottle, also, one and one-third ounces of 
red prussiate of potash in eight ounces of water ; keep 
in another dark bottle ; when about to use mix an 
equal quantity of each in a cup and apply in a dark 
room with a soft brush or sponge to one side of white 
rag paper, similar to envelope paper, let it dry and put 
away in a dark place until required for use. 







•■ 'EiiP^^^M^s^^^B 


1 


DRAWING 
OhHCE RULES 




^^^^^B9 


^ 


SI 



Qrawing Qffiee Rules,* 

There are drawing offices where from ten to nearly one hundred people are busily employed in m^vking 
new plans and sketches by the hundreds, and where thousands of completed drawings are filed for reference 
or for changes, as these are needed in the shop management. 

To be introduced for the first time into such a company is a trial for the " new man " both of nerve and 
manners, and a test as well of skill ; nothing helps more at such a time than an acquaintance with the rules 
and routine of the office, for the old saying holds good in a drawing office, of " doing in Rome as the Romans 
do." The author of this book has felt this strangeness in a new position and so adds the following model-rules 
for the guidance of the student when first entering a regular position in an office where many are employed 
and where success depends upon a systematic ordering of the work in hand. 

SIZE OF DRAWINGS. CHARACTER OF DRAWINGS. 

1. The standard size shall be 23 inches by 36 4. Detail drawings shall, as far as possible, classify 
inches, subdivided into half, quarter and eighth sheets. the different kinds of works, such as castings, forgings, 

2. Full-size drawings shall be reserved, as far as shafts, levers, piping, etc. Different kinds of work 
possible, for general views and parts not capable of shall not be shown on the same detail drawing. 

being shown on smaller sheets. 

. ,, , 1 -1 1 ,, r -lit *NoTE.— A. W. Robinson, M.E., Montreal, must have all 

3. All shop detad shall, as far as possible, be credit for these admirable rules and regulations. They bring into 
shown on quarter and eighth sheets. a single focus the whole science and art of mechanical drawing. 

191 



192 



Hawkins' Mechanical Drawing, 



5. All shop drawings liable to repetition shall be 
traced and blue-printed. All temporary details, re- 
quiring only one copy, may be made on sketch sheets 
and press copied. 

6. A shop drawing is to be considered as an order 
or instruction to the shop, and not merely as a state- 
ment or illustration. For this purpose it must convey 
clearly and distinctly all the information necessary 
to make the article. 

7. Every dimension necessary to the execution 
of the work is to be clearly stated by figures on the 
drawing, so that no measurements need to be taken in 
the shop by scale. AH measurements to be given with 
reference to the base or starting point from which the 
work should be laid out, and also with reference to 
center lines. 

8. All figured dimensions on drawings to be 
plain, round vertical figures, not less than one-eighth 
inch high, and formed by a line of uniform width and 
sufficiently heavy to insure printing well. No thin, 



sloping, or doubtful figures, or diagonal-barred fractions 
will be tolerated. All figured dimensions below two 
feet to be expressed in inches. 

9. All center lines to be alternate dot and dash 
in fine black line. All dimension lines to be double 
dot and dash, with a central space for the figure, and of 
such strength as to show on blue-print more faintly than 
lines of drawing. Lines of drawing to be bold and 
clearly defined in proportion to the scale, and may be 
shade-lined by making the right-hand and bottom lines 
heavier. No ornamental shading or other " frills " 
allowed on shop drawings. 

10. Every drawing, whether whole or half-sheet, 
shall have the title, date, scale and number of the sheet 
stamped in lower right-hand corner, and the quarter 
and eighth sheets printed on top. 

11. The name of the drawing, as given in the 
title, is invariably to consist of two divisions in one 
line separated by a hyphen. The first division is to 
state the general name of the thing or machine, and 



Hawkins' Mechanical Drawing. 



293 



the second name is to clearly designate the part or 
parts represented (or if a general view should so state). 
The wording of titles should be submitted to the chief 
engineer or head draughtsman for approval. 

12. Each drawing shall bear the name of the 
draughtsman and examiner, the surname being used 
without initials. 

13. Drawings of piping details shall be made in 
diagram form, using standard symbols. 

14. AH detail parts for standard or repetition 
work shall be shown unassembled as far as possible. 

DRAWING SYMBOLS. 

15. Detail shop drawings should state: 

(a) The pattern number of every casting in plain 
figures of large) size than the dimension figures. 

(b) The material of which the parts are made, 
using symbols as follows : C.I. — Cast iron. W.I. — 
Wrought iron. M.S. — Machinery steel. H.S. — Ham- 
mered steel. Bs. — Brass. Bbt. — Babbit. Bz. — Bronze. 
C.R.S.— Cold rolled steel. 

Other materials write full name. 



(c) Finished surfaces will be indicated by " f " 
written on the line or surface to be finished. When 
not so marked it is understood that the part is to be 
left black or rough. In cases Avhere finish might be 
presumed but not required, follow the figured dimen- 
sions by the word "cast," if a casting, and " rough," if 
a forging. 

STANDARDS. 

16. The following standards shall be strictly 
adhered to as given in the tables noted : 

(i.) Table of standard diameters of shafting and 
key seats. , 

(2.) Table of standard stock sizes of rounds. 

(3.) Table of standard stock sizes of flat steel. 

(4.) Table of standard clearance fits. 

(5.) Table of standard symbols for notation of 
riveting. 

(6.) Table of standard symbols for pipe fittings. 

Also such other standards as may be adopted from 
time to time. 



194 



Hawkins' Mechanical Drawing, 



NUHBERINQ OF DRAWINGS. 

17. Drawers and filing cases shall be numbered 
consecutively. Drawers shall contain 100 sheets each, 
and filing cases 200 sheets each, and to be fully in- 
dexed. Drawings shall be numbered by a number in- 
dicating both drawer number and serial number in the 
drawer — thus, 7,604 is the fourth sheet in drawer 76, etc. 

18. Drawing numbers shall be checked off the 
index as required, and the index posted up in uniform 
handwriting by the clerk. 

19. Standard size drawings shall be kept in 
drawers and quarter and eighth sheets in filing cases. 
All drawings shall be indexed by an index sheet kept 
in each drawer or case, 

CHECKING. 

20. All drawings must be approved before being 
traced. When tracing is completed it will be given 
immediately to the chief draughtsman, who will have 
a preliminary print made and carefully checked, before 
being used. 



PATTERNS. 

21. All patterns shall bear the number of the 
drawing on which they are first detailed, followed by a 
serial letter, according to the number of patterns on 
the drawing. 

22. Standard patterns used repeatedly and liable 
to be ordered from in repairs must not be changed. 
Other patterns may only be changed when absolutely 
necessary and by order. When so changed they will 
bear the original number and letter, followed by A for 
the first change, B for the second change, and so on 
thus : 4860 AB is the second change in pattern 4860 A. 

SKETCH BOOKS. 

23. Each draughtsman will be supplied with a 
sketch book by the company, in which he shall make 
all his notes, calculations and data referring to his 
work, and under no circumstances shall notes of value 
be made on loose sheets. Each entry should invari- 
ably be commenced with the subject and date, and full 



Hawkins* Mechanical Drawing. 



195 



notes made of data on which the calculations were 
based, and the results obtained clearly stated. These 
books are to remain the property of the company. 

IN GENERAL. 

24. Changes in drawings, sketches or order lists 
issued to the shop shall only be made when authorized 
by the chief engineer, or, in his absence, by the chief 
draughtsman, and when so authorized shall be made by 
the order clerk. 

25. The names of all similar parts in order lists 
and drawings are to be uniform. 

26. Tracings must be kept in safe, for blue-print- 
ing purposes only. Office copies of blue-prints must 
be used for references. 

27. No drawing, print or photograph shall be 
taken from office without permission. 

NUHBERINQ WORKING DRAWINGS. 

There are a great many different systems used in 
indexing drawings, most of which have some good 



points, but very few are sufficiently elastic to cover a 
wide field. A plan based upon the decimal system of 
notation is very simple, and, as there is no practical 
limit to the number of subdivisions, it can be ex- 
panded indefinitely. Following are the main outline 
features of the system as adapted to the needs of 
drawing offices belonging to large works. 

The main division numbers, 000, 100, 200, 300, etc., 
are used respectively for all plans and general sheets 
referring to the division concerned. 100 includes 
general plans covering more than one department, 
and all small-scale plans with cross references to de- 
partments covered. 

The class or tens divisions contain general 
drawings of the subdivisions, the subclasses or units 
divisions being limited to details only. Further sub- 
divisions would probably be necessary in some cases. 
A card index with cross references and written by 
someone who knew what to do is an essential part 
of the system. 



tgS 



Hawkins' Mechanical Drawing. 




Fig. 263. 



G^^ciPing. 



Under this heading the author has grouped some information relating to a subject of wide interest and one 
sure to interest a student of mechanical drawing. 

The diagrams are intended for exercises in drawing, i. e., to be redrawn as parts of practice ; the text is to be 
studied not only for the good to be gained from the study of gearing, but as an example of the way in which 
written or printed descriptions are necessary to explain a subject illustrated by drawings. 



A gear is primarily a toothed wheel ; gearing is a 
train of toothed wheels for transmitting motions ; there 
are two chief sorts of toothed gearing, viz., spur gear- 
ing and bevel gearing. 

A spur zu/iee/ has teeth around the edge pointing 
to the center ; commencing at the center, a spur wheel 
may be said to consist of a hole, square, octagonal or 
round, for its axle or shaft ; a hub ; the web, body or 
arms ; a rim, and the teeth ; see fig. 263. 

A spur wheel has teeth on its circumference which 
run parallel to its shaft; wheels as shown in fig. 271 are 
termed helical wheels ; these are similar to spur wheels 



except their teeth are arranged upon different angles 
to the shaft. 

A bevel is a slant or inclination of a surface from a 
right line, hence a bevel wheel is one whose teeth stand 
beveling or at an oblique angle to the shaft, or towards 
the center ; see fig. 267. 

Miter wheels are bevel wheels of the same size, 
working at right angles with one another ; see fig. 268. 

The diajtieter of both spur and bevel wheels is 
measured and calculated neither from the outside nor 
from the bottom of the teeth, but on the pitch circle. 
When we speak of the diameter of a spur or bevel 



199 



200 



Hawkins' Mechanical Drawing. 



wheel, we mean the diameter of the pitch circle, with- 
out any reference to the form of tooth. 

T/te addendum circle of a toothed wheel is as 
shown in illustration, fig. 264 ; addendum means "some- 
thing added," and, as shown in the figure, it is the part 
added beyond the pitch " line " or circle. 

The pitch line is the most important one in gearing; 
the " pitch line " or " pitch circle " is supposed to be 
the working circle. This is shown in P — P in fig. 274. 

The periphery of a wheel is the extreme circum- 
ference, as N in fig. 274. 

All parts of gear-wheels consist of portions, to 
which have been given generally accepted names. 
Fig. 264 shows the " addendum circle " and the " pitch 
line " as marked. The teeth and rim are shown in 
white, and the other portions are indicated by the names. 

The circular pitch line, as opposed to the diametral 
pitch, is the same as the pitch circle. It is a line which 
bisects all the teeth of a toothed wheel. 

The rolling circle is the same as the circular 
pitch line. 



Diametral means pertaining to a diameter or the 
length of a diameter; hence a diametral pitch is a 
system of measures or enumeration based upon the 




^_ J,..- -clRfLE j„^/ 



Fig. 264. 

diameter instead of the circular pitch line ; it is used 
very generally in spacing for fine tooth gear. Wheels 
of this description usually have their teeth cut in a 
gear-cutting machine, i. e., medium and fine tooth 
gears. 



Hawkins' Mechanical Drawing. 



20 1 



A cog wheel is the general name for any wheel 
which has a number of cogs placed around its circum- 
ference. 

When the teeth of a wheel are 
made of the same material and 
formed of the same piece as the 
body of the wheel, they are called 
teeth ; when they are made of wood 
or some other material and fixed to 
the circumference of the wheel, they 




Fig. 265. 
are called cogs ; see fig. 265 



A pinion is a small wheel. When two toothed 
wheels act upon one another, the smaller is generally 
called the pinion. The terms trundle and lantern are 
applied to small wheels having cyhndrical bars instead 
of teeth. The teeth in pinions are sometimes termed 
leaves ; in a trundle, staves. See fig. 273. 

The wheel which acts is called a leader or driver ; 
and the wheel which is acted upon by the former is 



called ^follower or the driven. When a screw or worm 
revolves in the teeth of a wheel, the latter is termed a 
worm wheel or worm gear; see fig. 270. When a 
pinion acts with a rack having teeth, we speak of rack 
and pinion. When the teeth are on the inside of the 
rim, and not on the periphery, the wheel is termed an 
internal gear ; see fig. 272. 

Two wheels acting upon one another in the same 
plane are called spur gear ; the teeth are parallel with 
the axis. When wheels act at an angle, they are 
called bevel gear. 

Frictioti gear-wheels are those which communi- 
cate motion one to the other by the simple contact of 
their surfaces. 

In frictional gearing the wheels are toothless and 
one wheel drives the other by means of the friction 
between the two surfaces which are pressed together. 

Grooved friction wheels are used to give greater 
cohesion than can be obtained by the plain surface. 



202 



Hawkins' Mechanical Drawing. 




Fig. 266. 



Fig. 263 shows a pair of spur-wheels in 
gear. The dotted circles which meet are 
the rolling circles, called the " pitch line " 
or " pitch circle." 

A spur mortise wheel is similarly- 
shown in fig. 266; it is very like in ap- 
pearance to a spur wheel ; it differs essen- 
tially in that the teeth are separate cogs, 
fixed in singly to the rim ; see also fig. 265, 
page 201. 

Note. — The teeth of spur wheels cast ftom a 
pattern must of necessity be larger at one side than 
at the other, because the teeth must have taper to 
permit the extraction of the pattern from the 
mould ; therefore, in fixing wheels to gear, the 
large side of one should meet the smaller side of 
the other ; should the two large sides come to- 
gether the teeth will meet only at the large side, 
and the teeth will probably break away fixini the 
excessive strain on that point. 



Hawkins' Mechanical Drawing. 



203 



Skew gearing are bevel wheels working out of 
center; the teeth do not form radial lines from the 
wheel center. 

Fig. 267 shows a pair of bevel wheels in gear as 
described on page 191. A bevel mortise wheel, i. e., 
one having cogs inserted in its rim instead of teeth. 




Fig. 267. 



204 



Hawkins' Mechanical Drawing. 



A bevel wheel and pinion must be made to suit 
one another by both having teeth forming together an 
angle of 90°, therefore they are pairs, or proportioned 




Fig. 268, 



in the number of teeth one to the other. Any other 
proportion used would not exactly gear and would be 
termed a " bastard " gear. 



Fig. 268 represents a pair of miter wheels in gear ; 
it will be noted that the shafts, when connected, will 
be at right angles to each other, the wheels being in 
all particulars of the same dimensions; the figure 
answers the purpose of a much longer description, if 
given in words. 

A miter-wheel can easily be known by putting 
a square upon the face of the teeth, which are always 
at an angle of 45° with one another, irrespective 
of size. 

A miter-zvheel is a particular kind of bevel-wheel, 
the bevel being limited to an angle of 45° in each 
wheel. 

The curve of the teeth in bevel-gears, when cor- 
rectly formed, changes constantly from one end of the 
tooth to the other, therefore bevel-gears whose teeth 
are produced with a forced cutter are not theoretically 
correct 



Hawkins' Mechanical Drawing. 




Fig. 269 
represents a 
rack and pin- 
ion : the teeth 
in tnis torm of 
gear are shaped 
similarly to 
those in the spur 
wheel, shown on 
page 198, with 
the difference 
that the teeth 



205 

of one are on a circle and 
on the rack are made on 
a straight line. 

A flange or addition 
to the end of a tooth and 
the rim connecting ihem 
together is used to 
strengthen the teeth. This 
extends from the root to 
pitch line when the wheel 
and pinion are both 
flanged : if only one is 
flanged it extends from 
the root to the addendum. 




206 



Hawkins' Mechanical Drawing. 




Fig. 270 illustrates a worm and 
a worm wheel, sometimes called 
screw gears. This is a slow but 
powerful method of transmitting 
power, one revolution of the worm 
only moving the wheel the distance 
of one tooth and space. 

A worm gear is a spur wheel 
with teeth at an angle to the axis, 
so as to work with a worm which 
is a screw, or has teeth shaped in 
the form of a spiral wound round 
its circumference; the screw or 
worm is called an endless screw, 
because it never c«mes to a stop- 
ping place in the circumference of 
the wheel. 



Hawkins' Mechanical Drawing. 



207 




Fig. 271 represents a gear with helical teeth. It is similar to a spur wheel, and is used 

in place of same in heavy and slow moving machinery, the formation of teeth preventing — • 

in large measure — the jar or concussion noticeable in common spur gears. 

In recent years the speed at which gearing is run has been greatly increased. A 

striking instance is that of a pair of cast-iron helical wheels, 6 ft. 3 in. diameter, 12 in. 

wide, making 220 revolutions 

per minute, the speed of the 

pitch line being 4,319 feet per 

minute ; these wheels are run- 
M ning continuously and with 
^ little noise. There is also a ait 

gear in a mill in Massachusetts, 

30 feet in diameter, and the 

speed of pitch line is 4,670 feet Fig. 272. 

per minute. 

An internal or annular gear wheel is one in which the faces of the teeth are within 

and the flank without the pitch circle, hence the pinion operates within the wheel. 

See fig. 272. 

In internal geared wheels there is almost an entire absence of friction and consequent 

wear of the teeth, as compared to ordinary spur gearing. 




208 



Hawkins' Mechanical Drawing, 



Fig. 273 shows a crown-wheel which has pin teeth 
which are fixed by one end only, on its side face and 
gear into a trundle wheel. 




Fig. 273. 

A trundle wheel has no teeth, properly speaking. 
Instead of teeth, it has pins as shown on illustration, 
fig. 273, arranged like the rungs of a ladder between 
two walls. See page 201. 



Trains of Gears. — When two wheels mesh — that 
is, engage with each other — as in fig. 263, one axle 
revolves in the opposite direction to the other; but 
when internal gears mesh as shown in fig. 272, the shafts 
revolve in the same direction ; three or more gears run- 
ning together are often called a train of gears. 

Maximum speed of gears under favorable condi- 
tions for safety is comparatively — 

Ordinary cast-iron wheels, 1 ,800 feet per minute. 



Helical 

Mortise wood cog 

Ordinary cast-steel 

Helical 

Cast-iron machine cut 



2,400 
2,400 
2,600 
3,000 
3,000 



It is not, however, advisable to run gears at their 
maximum speeds, as great noise and vibration are 
caused. 



Resigning G^^''^- 



This section is introduced into the work for a double purpose; i, as an exercise in drawing; 2, as a study in 
accurate measurements. It is a sample of the work that the advanced student in mechanical drawing will be 
confronted with as he puts in practice the theory of the art of drawing. 

Some sample rules are given in the following pages to aid in calculations relating to gears, and still others are 
given under the section " Useful Rules and Tables " at the end of the volume ; these are to be carefully studied. 



To accurately divide the pitch circle of a gear 
wheel by hand requires both patience and skill. On 
the accuracy of spacing lies the essential requisite of a 
good gear wheel. 

The drawing in plate, fig. 274, illustrates a pair 
of spur wheels, shown in gear, the office instructions 
for which being : 

" Required, a detail plan of a pair of spur wheels ; 
dimensions : wheel, 76 teeth, 3^ inches pitch, 7-inch 
eye, 6 arms; pinion, 19 teeth; scale, i^ inches — i 
foot." 



The drawing, as illustrated, is the result of the 
above instructions, all pencil lines being removed, and 
this result is worked out as follows : 

76 teeth X 32" inches, pitch ^266 inches in circum. 
= 7 ft. .0^ ill- diam.^3 ft. 6^|- in. radius ; with this 
measurement as represented on scale, draw line P P on 
drawing. This is called the pitch line. 

Draw next diameter line, produce or extend this 
diameter line for pinion, and with radius of 10^ (19 
teeth X3i) from pitch line of wheel, draw pitch line of 
pinion. 



209 



2IO 



Hawkins' Mechanical Drawing. 



Take any point in this pitch line of wheel, mark 
off 3^ inches as represented on scale, mark this around 
the pitch line, it will be the center of each of the y6 
teeth ; then the breadth of thickness of each tooth 
(= pitch X 0.475) must be marked from these centers, 
then mark from P L, length of tooth to point ( = pitch 
XO.35) and P L to root (^ pitch X0.4), draw circles for 
outside of teeth N and root of tooth O ; now with 
compass set to the pitch (3J) of the wheel, draw the 
outer portion from pitch line of tooth. 

The radius will center in the pitch line of next 
tooth where thickness of tooth has been marked ; after 
finishing outer portion of both sides of teeth, set the 
compass from center of tooth with radius to the thick- 
ness marked on pitch line and draw the portion of tooth 
from pitch line to root. 

Now mark off with dividers and draw thickness of 
rim (= pitch X0.5), divide this line into six parts, draw 
radii for centers of arms ; draw the bore hole 7" and 
the thickness of metal for hub same as pitch. 



On radii lines of arms, draw the breadth of arm at 
rim (^ pitch and thickness of tooth), increase in breadth 
approaching the center (i" per foot), draw the thick- 
ness of feather of arm (^ pitchXo.35) ; draw web on 
inside of rim (= pitch X 0.375) ; fill in arcs for the join- 
ing of arms in rim and hub (radii ^ pitch X 0.8) and 
feather to rim and hub (radii = pitch X 0.37). 

Proceed in similar manner, completing the teeth 
of pinion, and when pencil lines are all in, ink the draw- 
ing, erasing all needless lines. 

P P shows the pitch line ; B, thickness of tooth ; 

c, breadth of space; A, the pitch ; £, clearance at root; 

N, the addendum of tooth ; O, the root of tooth ; H, 

length of tooth from pitch line to point ; /, length of 

tooth pitch line to root ; G, whole length of tooth ; F, 

thickness of rim ; /, web or feather on rim ; K, breadth 

of arm; L, thickness of feather: 3f, hub, or thickness 

round the eye. 

Note. — It must be remembered that no fixed standard has 
ever been agreed upon for these proportions, and workshops dif- 
fer considerably in practice. 



Hawkins' Mechanical Drawing. 



21 I 




Fig. 274. 



212 



Hawkins' 



Mechanical Drawing. 

B 



--] 




The number of teeth, their 
proportions, pitch and diameter of 
pitch circle are frequently deter- 
mined on the "Manchester" prin- 
ciple. This system originated in 
Manchester (Eng.), and is now 
generally used in the United States 
for determining diameters and 
number of teeth, which, of course, 
regulate speeds. The principle is 
not applicable to large wheels, but 
is limited in its application to small 
wheels, or wheels having " fine 
pitch," as will be seen in the fol- 
lowing explanation, which is in- 
troduced as verj' useful and indis- 
pensable knowledge for the acqui- 
sition of the student in mechanical 
drawing. 

The "pitch" of teeth has 
already been stated to be the dis- 
tance from center of one tooth to 
the center of another on the " pitch 
line," measured on the chord of 



Hawkins' Mechanical Drawing. 



213 



the arc. In determining the number of teeth or pitch 
of wheels on this principle, the pitch is reckoned 
on the diameter of the wheel, in place of the circuvt- 
ference, and distinguished as wheels of '" 4 pitch," " 6 
pitch," " 8 pitch," etc. In other words, this means 
that there are are four, six, or eight teeth in the cir- 
cumference of the wheel for every inch of diameter. 

In designing gears to transmit power the stress on 
a tooth is calculated ; it determines the breadth or 
width and also the thickness of the tooth on pitch line ; 
the space between the teeth is in proportion to the 
thickness of tooth, and the thickness of both combined 
(one tooth and one space), measured on the pitch line 
or circle, is the pitch of the wheel. 

From the pitch all the proportions and measure- 
ments for the sizes and strength of the parts of the wheel 
are taken by rule, and a symmetrical form is produced. 

In machine drawing the practice is to represent 
wheels by circles only ; the teeth are never shown 
except on enlarged details and then only in very rare 



instances; the circles drawn are always the pitch lines 
or the rolling points of contact of the wheels. 

The addendum circle is seldom if ever used in 
practical drawing. Should it be necessary to show it 
in an exceptional case, the circle would be represented 
by " dotted " line. 

The shape of tooth and mode of constructing it, 
as practiced in drawing offices, differs from the true 
theoretical curve of the tooth, although very minutely. 

In all calculations for the speed of toothed gears the 
estimates are based upon the pitch line, the latter stand- 
ing in the same place as the circumference of a pulley. 

To find the diameter of a gear-tvJieel multiply the 
number of teeth by the pitch, divide by 3. 1416. 

To find Xhe pitch of a gear.tvhecl multiply the dia- 
meter by 3.1416 and divide by the number of teeth. 

To find the member of teeth in a o^ear-wheel multiply 
the diameter by 3.1416 and divide by the pitch. 

The breadth of zvJicels, where practicable, should be 
at least three times the pitch. 



214 



Hawkins' Mechanical Drawing. 



o 












\\\\v\v\^° 








M 


n\\\M\l\KK 


K^ 








1 \ \\ \W 




INCHES 


\ \ \ Xb 


^ 


\\ 10 




ro 


n \ \ \ 


\\^ 


\r\ \ 




- 


u\\ 


\\ 


\\\ 


\^ 




W 


\\= 


\\ 


\ \ \^10 


w ~ 


1 \ \ 


\l \ 


\^ 


\ \ \ \ 



10 DIVISIONS. 
Fig. 276. 



Fig. 276 shows a scale for proportions of teeth ; it 
is divided into tenths and used thus: 

Say wheel is 2" pitch, then from pitch circle to 
addendum will be 3>^ tenths, and from pitch circle to 
root of tooth will be 4 tenths measured at the 2 ' line 
on scale, and so on. 

The decimal proportions already given in example, 
page 210, are adopted in many workshops. Many 
others use the proportions approved of by Sir William 
Fairbairn, which are : 

Table of proportion of gears : 

Depth of tooth above pitch line. . . 
" below pitch line. . . 

Working depth of tooth 

Total depth of tooth 

Clearance at root 

Thickness of tooth 

Width of space 



•35 « 


3f the pitch 


.40 




.70 




•75 




.05 




•45 




.55 


n 



Hawkins' Mechanical Drawing. 



215 



The diameter of a wheel or pinion is invariably the 
diameter measured on pitch circle, except it is specially- 
described otherwise, thus the diameter "over all," etc. 

The shape of the curved face of the teeth of gears 
extending from the root to the addendum is the curve 
conforming to the passage of the teeth described on 
its fellow entering and leaving, as they rotate or roll 
together on their pitch circles. 

The curve of teeth outside the pitch circle is called 
" the face," and the curve from pitch circle to root is 
called " the flank." 

The difference between the width of a space and 
the thickness of a tooth is called clearance or side 
clearance. 

The play or movement permitted by clearance is 
called the backlash ; clearance is necessary to prevent 
the teeth of one wheel becoming locked in the spaces 
of the other. 

Wheels are in gear or geared together when their 
pitch lines engage, t. e., when the pitch circles meet. 



Wheels to be geared together must have their 
teeth spaced the same distance apart, or in other 
words, of the same pitch. 

The teeth of spur wheels are arranged on its 
periphery parallel to the wheel axis, or shaft on which 
it is hung. 

The teeth of a bevel wheel or bevel gears are 
always arranged at an angle to the shaft. 

When the teet/i of bevel gears form an angle of 
45° they are called miter wheels. 

Miter wheels to gear must be of equal sizes. 

A crown wheel is a disc that has teeth which are 
on its side face; that is, teeth on a flat circular 
surface all parallel to the axis of the wheel. 

A rack has teeth on a flat surface or plane all 
parallel to one another. 

A gear cut by machine is called a cttt gear. It has 
teeth with less clearance than cast wheels, which are 
not so true or perfect, and therefore require more 
clearance. 



2l6 



Hawkins' Mechanical Drawing. 



A worm with even a light load is liable to heat 
and cut if run at over 300 feet of rubbing surface 
travel. The wheel teeth will keep cool, as they form 
part of a large radiating surface ; the worm itself is so 
small that its heat is dissipated slowly. 

A worm throws a severe end thrust or strain on 
its shaft. 

Stee/ Gears. — There is great economy in the use 
of cast-steel over cast-iron in gears ; the average life of 
the former is nearly twice as great as of cast-iron gears. 
And, apart from their longer life and efficiency, there 
is less danger of breaking. 

The most accurate teeth, strongest and most 
uniform in wearing, are to be found in steel gears cut 
from solid stock, or made by cutters of proper shape. 

Fig. 275 shows an elevation and a vertical section 



of a spur wheel. From these views the various parts 
in spur gears can be better understood, as they are 
represented here in combination, and the wheel in its 
entirety. 

A A is the horizontal center line, BB, BB the ver- 
tical center lines, // and // the pitch lines, N thickness 
of tooth, O space of tooth, D total depth of tooth, 
C breadth of face, F diameter on pitch line, P diameter 
overall, G diameterof hub, E diameter of hole, //'depth 
of hole, L thickness of rim, M thickness of web. 

Much has been and still is being written on gearing. 
No general rule is followed by the writers ; the elemen- 
tary principles given will enable the student to master 
spur gearing, and bevel and combinations of many 
kinds of wheels will afterwards be found easier to 
delineate than the numerous lines seem to indicate. 



2l8 



Hawkins' Mechanical Drawing. 




Fig. 277 



\^orI^ing I^pawings. 



From the " plans " made in the office are produced " working drawings " — which represent in detail the work 
to be done to exact measurement and of material, as indicated, by the pattern-maker, the foundr}.-, the forge, the 
shop, and finally, by the erector of the completed mechanism. 

How to satisfactorily fuliiU the directions contained in these drawings, representing only a part of the work, so 
that it will fit, with needed accuracy, to all other parts of the design, is the task before each separate worker. 



It is by means of this division of the process of 
manufacture through these drawings, that scores and 
hundreds of men can be employed at the same time 
upon a single engine or machine; thus, while hand- 
work has been superseded by machines in many quar- 
ters, the art of drawing has not been narrowed nor 
diminished, for no drawings or designs have yet been 
made by machinery, nor are they likely to be. 

It is thus that a good designer and draughtsman 



"projects" or extends himself, to the advantage of 
many fellow workers. 

The drawing, fig. 277, shows a simple form of pillar 
crane ; it consists of an upright cast-iron pillar, which is 
bolted on a cap stone, under which is the foundation plate 
not shown in the drawing ; the boom is of rolled steel, 
supported by steel tie rods, and provided with rollers 
at the base ; the hoisting gear is shown in broken 
lines and circles ; all as seen in the drawing. 



219 



220 



Hawkins' Mechanical Drawing, 




Fig. 278. 



Fig. 279. 



Hawkins' Mechanical Drawing. 



221 



'© & 6J 

p d djo (3 (S) 

Q Q 




Fig 280. 



Figs. 278, 279 and 280 show a drawing 
of a " hydraulic beam bending machine " in 
three views ; fig. 280 is a plan, fig. 278 is an 
end elevation, and fig. 279 a side elevation, 
and a portion of the latter in section shows 
the interior construction. 

Note. — These three ^•iews are a practical illus 
tration of drawings for a machine of the following 
dimensions : this machine has a bed 3x5 feet in area, 
with 27 holes in each side for the bending pins. The 
frame and cylinders are made of cast iron, the rams of 
machinery steel, and the slides for holding the bend- 
ing blocks, of steel casting. The distance between 
the bending blocks is 17 inches. The cylinders are 
copper lined, 8 inches diameter, and the rams have 
a 6-inch stroke. The rams, which are independent 
and single acting, are returned by counterweights 
placed as shown under the table. The cylinders can 
be operated independently from either side of the 
machine by an arrangement of valves and levers. 
The machine complete weighs about 7,500 lbs. 



222 



Hawkins' Mechanical Drawing. 




Vift. 281. 




Fig. 282. 




Fig. 283. 



Hawkins' Mechanical Drawing. 



223 



The drawing, page 222, shows three views of a 
power punching press. 

Fig. 282 is a side elevation. 

Fig. 283 a front elevation. 

Fig. 281 a vertical sectional view ; from these views 
the proportion, general arrangement and disposition of 
the automatic devices can be easily understood ; it may 
be well to call particular attention to the automatic 
clutch on the top shaft and the tripping device. 

This drawing, fig. 284, shows a side elevation in 
section of a self-adjusting piston-rod packing. 

A is the gland, B is the piston rod, C" is a brass 
sleeve which contains the packing D, E is the cylinder 
cover, F'lsz. coil spring. It will be seen that the spring 
i^ abuts on a bushing in the bottom of the stuffing box 
and is prevented from scoring the piston rod by step- 
ping over the ends of the bushing and follower. All 
as shown in the drawing. 




Fig. 284. 



224 



Hawkins' Mechanical Drawing. 



The drawing, fig. 285, shows a sectional view of a 
large pulley fixed on a " quill," or hollow shaft ; the 
driving shaft passes through the hollow shaft and is 




Fig. 285. 



attached to the friction clutch shown at the right-hand 
end ; this friction clutch drives the hollow shaft and 
pulley. 



Hawkins' Mechanical Drawing. 



225 



Fig. 286 shows the mechanism, called the link-motion, employed to reverse an engine, or to enable it to be 
run in either direction. Many forms of link-motion have been devised, but the Stephenson form, as shown in the 
figure, is, however, the one in almost universal use. 




Fig. 286. 
This drawing shows shading and the mode of figuring the parts for identification. 



226 



Hawkins' Mechanical Drawing, 




Deacimarr or Anchor 
Frorrr Elevation, 



Side 
Elevation . 



Fig. 287. 



Kg. 288. 



Fig. 289. 



Hawkins' Mechanical Drawing. 



227 



Figs. 287 to 289 represent a bumping-post for 
the end of railway tracks, reproduced on an enlarged 
scale from the columns of the Engineering News. 

In addition to the lettering and dimensions, admir- 
ably shown in the drawings, the following description 
is appended to show how printed text and mechanical 
drawings mutually aid in practical — or commercial — 
usage. 

The unique feature of the arrangement shown, 
is that the center line of the post does not coincide 
with the track, thus adapting itself to the nature of 
the blows of a car-bumper, as received in the single- 
post style of the mechanism. 

BUMPING POST FOR RAILWAY TRACKS. 

The post is a 15-in. steel I-beam, resting on a base 
plate yi-in. thick, and supported by anchor rods l^ins. 



diameter, with upset ends held by nuts on a heavy 
forging bolted to the top of the post. These rods 
extend forward and outward to clear the rails, and then 
pass vertically through a 4X6-in. angle iron crosstie, 
and an ordinary wooden tie, extending down to an 
anchor block or deadman buried in the ground 6}^ ft. 
below the top of the rail. 

Vertical braces or spreaders are fitted between the 
anchor timber and a longitudinal timber under the ties, 
so as to prevent the loosening of the anchor rods when 
the post is struck. The rods are held in position 
against the rails by steel forgings bolted to the rail 
with i-in. turned bolts. An oak striking block, 12X12 
ins., 3 ft. long, is bolted between angle iron brackets 
on the face of the post. 



228 



Hawkins' Mechanical Drawing. 





Fig. 290. 




Fig. 291. 




Front View. 



Scale, 3 in. = I ft. 



Side View. 



^o Read \/V)orI^ing Qrawings. 



One of the advantages resulting from a knowledge of practical draughting is, that it enables a mechanic to 
read a drawing when given him as a guide for his work. It is getting every day more general among draughtsmen 
to figure exactly and minutely every part of their drawings which are made to a scale. 



Drawings are almost always made " finished size," 
that is, the dimensions are for the work when it is 
completed. Consequently all the figures written on 
the different parts indicate the exact size of the work 
■when finished, without any regard to the size of the 
drawing itself, which may be made to any reduced and 
convenient scale. 



Even in full size drawings this system of figuring 
is not objectionable. It is a system which should be 
followed whenever a drawing is made "to work to," 
for it allows the workman to comprehend at a glance 
the size of his work and the pieces he has to get made. 
Figuring makes a drawing comprehensible even to 
those who cannot make drauings. 



229 



230 



Hawkins' Mechanical Drawing. 



A working drawing should be made, primarily, as 
plain as possible by the draughtsman ; second, the 
workman should patiently and carefully study it, so 
that it is thoroughly understood. 

In studying a drawing, the object it is intended to 
represent should be made as familiar as possible to the 
mind of the student, so that he may fill out in imagi- 
nation the parts designedly left incomplete — as in a 
gear wheel where only two or three teeth are drawn in, 
that he may see, mentally, the whole. 

The following is a description of reading drawings 
when dimensions are not figured. Here we have a 
piece of machinery represented by fig. 290, and the 
information we have is that it is to scale, three inches 
= one foot. Now, with scale and dividers, we can 
arrive at its actual dimensions. 

Measurements should be first taken wii/t the 
dividers from the drawing, and then the dividers 



applied to the scale to which the drawing is made ; 
this scale is always marked on the working drawing ; if 
the dividers are set to the length of the base of the 
example, fig. 290, they will measure, on an ordinary 
two-foot rule, three and three-fourths inches, but if 
applied to the three-inch scale they will read one foot 
three inches, the actual length of the part ; the " read- 
ing " is from the scale ; thus, in both figures the draw- 
ings are " three-inch scale." 

Now, 3 inches is one-fourth of a foot, hence 
3^X4^1 ft. 3 in., the full size, and so on for all 
parts of the drawing. 

Fig. 291 shows a side view of the "steady rest," 
illustrated in front elevation, fig. 290 ; from the scale 
as before we get the sizes ; the two views combined 
give length, breadth and thickness of the parts. 

In some figures it is necessary to show end views, 
also section views, to enable all measurements to be 
read from the drawing. 



Patent Qffiee [^rawing Rules. 



U. S. PATENT OFFICE RULES. 

AS APPLIED TO PREPARATION OF DRAWINGS. 

Each applicant for a patent is required by law to 
furnish a drawing of his invention whenever the nature 
of the case admits of it. The drawing must be signed 
by the inventor or the name of the inventor may be 
signed on the drawing by his attorney-in-fact, and in 
either case must be attested by two witnesses. The 
drawing must show every feature of the invention 
covered by the claims. 

When the invention consists of an improvement 
on an old machine, the drawing must exhibit, in one or 



more views, the invention proper, disconnected from 
the old structure, and also, in another view, so much 
only of the old structure as will clearly show the con- 
nection of the invention with the old machine. 

Several editions of the patent-drawings are printed, 
the smallest of which is about 3x4!- inches, so that the 
drawing must be so made that it will stand a reduction 
of about one-fourth. This work is done by the photo- 
lithographic process, and therefore the character of the 

Note. — These rules will be found most useful to many 
readers of this work — hence their introduction at this point 
Nearly 50,000 patents are " appUed for" in the United States 
every year. 



2.^^ 



234 



Hawkins' Mechanical Drawing. 



original drawing must be brought as nearly as possible 
to a uniform standard of excellence suited to the 
requirements of the process. 

The following rules are given by the Patent Office 
for guidance : 

1. Drawings must be made upon pure white 
paper of a thickness corresponding to three-sheet 
Bristol board. The surface of the paper must be 
calendered and smooth. India ink alone must be used, 
so as to secure perfectly black and solid lines. 

2. The size of a sheet on which a drawing is 
made must be exactly 10x15 inches. One inch from 
its edges a single marginal line is to be drawn, leaving 
the " sight " precisely 8x13 inches. Within this margin 
all work and signatures must be included. One of the 
shorter sides of the sheet is regarded as its top, and 
measuring downwardly from the marginal line, a space 
of not less than i^ inches is to be left blank for the 
heading of title, name, number and date. 



3. All drawings must be made with the pen only. 
Every line and letter, signature included, must be 
absolutely black. This direction applies to all lines, 
however fine, to shading, and to lines representing cut 
surfaces in sectional views. All lines must be clean, 
sharp, and solid, and they must not be too fine 01 
crowded. Surface shading, when used, should be open. 
Sectional shading should be made by oblique parallel 
lines about ^ of an inch apart. Solid black should not 
be used for sectional or surface shading. 

4. Drawing must be made of the fewest lines 
possible, consistent with cleanness. The plane upon 
which a sectional view is taken should be indicated by 
a broken or dotted line. Heavy lines on the shade 
side of objects should be used, except where they tend 
to thicken the work and obscure letters of reference. 
The light is always supposed to come from the upper 
left hand corner at an angle of 45 degrees. 

5. The scale to which a drawing is made should 
be large enough to show the mechanism without 



Hawkins' Mechanical Drawing. 



235 




Fig. 29Z 



236 



Hawkins' Mechanical Drawing 



crowding. The number of sheets used must never be 
more than is absolutely necessary. 

6. The different views should be consecutively 
numbered. Letters and figures of reference must be 
carefully formed. They should, if possible, measure 
at least one-eighth of an inch in height. 

If the same part of an invention appears in more 
than one view of the drawing it must always be repre- 
sented by the same character. 

7." The signature of the inventor is to be placed 
in the lower right-hand corner of each sheet, and those 
of the witnesses at the lower left-hand corner. 

The title should be written with pencil on the back 
of the sheet. 

Drawings should be rolled for transmission, never 
folded. 

On page 235, fig. 292 exhibits a reproduction of a 
patent office drawing, used in connection with specifi- 



cation papers in an application for a United States 
patent. 

ENGLISH PRACTICE. 

The rules for patent drawings in England are 
practically the same as in the United States ; the 
paper sizes are, however, different. They must be on 
sheets of one of the two following sizes (the smaller 
being preferable), 13 inches at the sides b)' 8 inches 
at the top and bottom, or 13 inches at the sides by 16 
inches at the top and bottom, including margin, which 
must be one-half an inch wide. 

If there are more figures than can be shown on 
one of the smaller-sized sheets, two or more of these 
sheets should be used in preference to employing the 
large size. When an exceptionally large drawing is 
required, it should be "continued" on subsequent 
sheets. There is no limit to the number of sheets that 
may be sent in. 



i 











PRACTICAL POINTS 


■ 


(^^^g 




9 



238 



Hawkins' Mechanical Drawing. 




Fig. 293. See page 244. 



Useful joints and '^points." 



Many of these " points " are repetitions, with but Httle variation from the way they have been previously 
stated ; they are thus repeated to emphasize their practical worth. 



A good draughtsman leaves his work in such a 
state that any competent person can without difficulty 
ink in what he has drawn. 

The criterion of a good set of drawings is that 
with a properly prepared specification they are com- 
plete in themselves and require no explanation. 

A " break " in a figure or object in a drawing is 
shown in rough irregular lines, as in fig. 134, on page 
131 ; this is useful when the paper is not large enough 
to show the whole. 



Never use a sloping line in writing fractions on a 
drawing. The objection arises from the fact that such 
a dimension as i^^^, if written with the inclined line, 
unless verj^ distinctly executed, may be read as -^f . 

In inking do not draw the lines further than you 
wish them to go, but in penciling it is well to extend 
the lines, free up. 

. Never use a scale for a ruler. 

Do not ov^erload the pen with ink. 



239 



240 



Hawkins' Mechanical Drawing. 



Having filled the pen, nearly close the nibs and 
try the width of the line on a piece of paper or the 
margin of the drawing. 

Never refill or lay the pen aside without first clean- 
ing it. 

The application of the science of geometry to the 
drawing-board is absolutely necessary to success, for 
the reason that the whole fabric of mechanical drawing 
rests on the principles of geometry, which is well 
termed the science of measurements. 

Section lines should be the last inked and always 
without previous penciling. 

Center lines are necessary in working drawings. 

In choosing T-squares, care should be exercised to 
see that the head slides up and down the /e/t-hand side 
of the board easily, and that when pressed against the 
board with the left hand there is no " slogging " of the 
blade up or down, or in other words, that the head is 
bearing firmly for its whole length against the board. 



The best place for the title of a drawing is said to 
be the upper left-hand corner ; this facilitates the filing 
of the sheet. 

Never use a soft pencil except for finishing in 
shadow lines. 

The rubber should always be kept clean. 

Great care should be taken to keep drawing boards 
out of the way of heat or damp, as these cause the 
wood to warp. 

Circles and curves are to be " inked in " before 
straight lines. First ink the smallest and afterwards 
the larger curves. 

Do not press heavily on the pencil so as to cut the 
paper, but draw lightly, so that the mark can be erased 
and leave no trace, especially if the drawing is to be 
inked. 

The draughtsman should commence his work at 
the top of the paper, keeping the lower part covered 
over until he needs to use it. 



Hawkins' Mechanical Drawing. 



241 



Shade lines should be avoided in all working 
drawings, as their use interferes with accurate measure- 
ments. 

To make ink stick to the tracing cloth, with a 
woolen cloth rub some powdered chalk or pounce over 
the surface on which the ink lines are to be drawn, then 
wipe the surface clean and use a good quality of ink. 

For striking small circles a small bow pen should 
be used. 

To fix lead pencil marks on sketches so that they 
cannot be readily erased, sponge them with milk care- 
fully skimmed, then lay blotting paper over them and 
iron with a hot flat-iron. 

To have the ink preserve its fluidity and to keep 
out all dirt and dust, keep the cover on the ink slab ; 
the mistake is often made of putting too liberal a sup- 
ply of water in ink well, which causes a waste of both 
time and ink; no more should be prepared than to 
meet immediate requirements. 



Always draw on the right side of the sheet, which 
can be found by holding the sheet up to the light and 
looking across its surface with the eye nearly in the 
same plane as the paper ; note which side is the smooth- 
est and has the least number of blemishes on it ; this is 
the right side to draw on. 

As to sharpening pencils, it is always best to cut a 
chisel point on the pencil used for drawing, and put a 
circular point on the pencils in the bow pencil and 
pencil leg. The chisel point makes a finer line and 
lasts much longer than a round point. 

The varnish used in many large drawing-rooms is 
simply white shellac dissolved in alcohol ; it requires a 
little experience to mix these to a proper consistency, 
but this is soon acquired. 

Never sharpen your pencil over the drawing. 

A center line of a drawing is the line upon which 
the figure is to be constructed ; the center line is the 
first line to be drawn. 



242 



Hawkins^ Mechanical Drawing, 



The T-square belongs to the left side of the draw- 
ing-board, and is operated by the left hand. The right 
hand should be kept free for the purpose of picking up 
pencil, pen and bows, adjusting and marking off. The 
left hand controls the T-square and the triangle that 
slides along the upper edge of the square ; the right 
hand is for the instruments. 

The advantage of a paper rule or scale is that the 
paper will expand and contract under varying degrees 
of atmospheric moisture the same as the drawing does. 

Avoid rubbing out and constantly cleaning the 
drawing with India rubber ; if wrong lines are made or 
it is desired to make alterations, the part to be changed 
should be rubbed out and completely re-drawn. 

When using the bows see to it that the steel- 
pointed leg that is put down first on the paper, to 
secure a center for a curve or a circle, is a trifle longer 
than the pencil or pen leg. 

To clearly indicate the position of a center which 
is to be used again, lightly pencil a small circle about 



it ; never put the point of a pencil in the center hole 
to enlarge or blacken it ; th prick point made by the 
dividers and needle points should be no more than can 
be just seen, hence the circle to be made as advised 
above. 

Be particular in having the legs of the dividers 
exactly the same length, and sharp, so that in pricking 
ofl distances, and dimensions, and centers, the indent 
or hole made in the paper is as small as possible. 

The term " plane " means a perfectly flat surface ; 
that is, something which has length and breadth but 
no thickness. 

The best way to indicate on the drawing the sur- 
faces which are to be finished is to write on the lines 
which represent the finished surfaces " finished," tool- 
finish, or '•' faced," according to the degree of finish re- 
quired. The single letter y^ is frequently used. 

Avoid fingering the drawing sheet as much as pos- 
sible ; in pointing to any part of the drawing use a 
pencil and not the finger. 

Remember that a drawing is made to be read. 



Hawkins' Mechanical Drawing. 



243 



The skill in inking does not depend on the fineness 
of the line, but on its clearness. 

A soft pencil should never be used on a mechanical 
drawing unless in rare cases when it is used for pencil 
shading ; the hardness or softness of pencils is denoted 
by letters. 

Never ink any portion of a drawing until the 
penciling is entirely finished. 

Stretching or pasting the paper to the board is 
very seldom resorted to, for the reason that the 
mechanical drawings are to scale and the paper is 
natural when pinned to the board and more correct 
than if under a strain. Mechanical drawings are 
always required in practice rigJit away, and time would 
be wasted and lost in damping and pasting and drj'ing 
again. 

A working drawing, whether made to a scale or 
not, must have all the dimensions plainly written upon 
it, for a workman should never be compelled to measure 
a drawing. 



In marking off distances, centers, etc., a fine needle 
point is useful ; the hole should not be punctured 
through the paper, merely a prick point, so that it 
will leave an impression, which will not be obliterated 
by the use of rubber; drawing-pens are often equipped 
with such a needle point in the end of the handle, 
that is visible only when the pen is unscrewed from 
the handle; but in the absence of one of this kind the 
point of the divider leg will be of use. 

Mechanical construction drawings represent a large 
amount of mental and manual work, as well as a con- 
siderable cost in money ; hence, they are of value quite 
as much as property which has been acquired by the 
expenditure of either labor or capital. It is wise to 
keep copies of original designs and sketches, as well as 
data and formulae, for record and comparison. 

The best system for keeping drawings is to make 
them of certain standard sizes, and to keep them flat, 
unrolled, in drawers, numbered, lettered and labeled. 



244 



Hawkins' Mechanical Draw in 



In an office where space is limited and drawings 
have to be rolled it is well to use a number of paste- 
board cases about three feet long and three inches in 
diameter. These are shown in fig. 294. 

A puncture can be made near the top and, when a 
new drawing or blue-print is inserted in this cylindrical 
case, a cardboard tag can be looped through the punc- 
ture. This label will give the title and number of 
drawings in that case. 

A manuscript book methodically and neatly kept 
should tell immediately the number of the drawing 
and the case. 

Fig. 293 is good for practice in line drawing and 
also as an optical illusion. "You look and are de- 
ceived. At first glance you say, ' Of course, those two 
lines are curved.' You are mistaken. They are exactly 
parallel. In order to prove this hold them up edgewise 
to the eye. It is, of course, the subsidiary lines which 
lead the vision astray. It is a case of first impressions 
being quite wrong." 



Fig. 294. 



f^^H 








LINEAR PERSPECTIVE 


^^^^9 


I^^H 


^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^■' ""^^^^^^^^^^^^H 





246 



Hawkins' Mechanical Drawing. 



!>0'-T''. 



%^5S 




Fig. 295. 



[iineap pepspeetiv)e. 



It should be mentioned that this subject is outside 
the limits of mechanical drawing, which only deals 
with objects that can be measured, projected or 
dimensioned to an accurate scale. 

But, in rounding out the more formal subjects it 
is well to look a little outside the rigid lines of me- 
chanics into the methods of nature, for no system of 
teaching drawing is complete that does not include 
some explanations for sketching from nature — the 
objects being always around the student, the eye 
always clear to see and the hand only needing 
the training to make permanent the impressions re- 
ceived. 

The word perspective means to see through ; the 



word perspective being derived from the Latin word 
perspicere, to look through, hence, perspective is a 
science which teaches us to see correctly and enables 
us to represent the appearance of anything we may 
wish to draw ; care should be taken in perspective 
drawing, to select objects interesting in themselves, and 
the best specimens of their class, so as to cultivate 
taste, while they at the same time afford useful and 
instructive drawing lessons. 

The meaning of the term linear perspective is a 
line view ; the previous examples have been composed 
of surfaces placed fronting the eye ; perspective is the 
science which treats of the changes of form produced 
by viewing them in various oblique positions. 



247 



248 



Hawkins* Mechanical Drawing. 




Fig. 296. 



The slightest alteration of po- 
sitioTi will change the appearance 
of an object; this can be easily- 
shown — for illustration take a coin, 
the actual shape of which is a 
perfect round ; or, strictly speak- 
ing, a circle. If we take the coin 
between the thumb and the first 
finger, holding it in an upright 
position, and exactly facing the 
eyes, as in Fig. 296, it appears of its true form, viz., a 
circle. If we alter its position, balancing it upon the 
thumb, in a level position, with its edge directly oppo- 
site the eye, as in Fig. 297, its appearance is changed, 
and what we know to be really a circle, appears to us 
as a straight line. 

Now, still balancing the coin upon the thumb, but 
changing its position with regard to the eye, by holding 
it a little lower than in the last position, that is slightly 
beneath the level of the eye, as in fig. 298, we see both 



the edge and the surface, the coin now appearing 
neither a circle nor a straight line, but a curved figure 
of an elliptical form. Thus the same coin held in three 
different positions has assumed three different shapes. 

Let us take two coins of the same size, holding (in 
the position shown at fig. 296) one in each hand. Now, 
closing one eye, (which will make the experiment more 

clear), hold one coin out 
at arm's length, and the 
other at about the distance 
of a foot from the eye. 
On comparing them, we 
Fig. 297. find that the coin which 



is further from the eye 
appears less than the 
nearer one. We know that 
the coins are really equal 
in size, yet one appears 
smaller than the other. 





Fig. 298. 



Hawkins^ Mechanical Drawing, 



249 



We thus see that when we change the position of 
an object, we have as a consequence a change of 
appearance ; also that the change of appearance may 
affect both the shape and the size of the object. 

These diversities of appearance may be remarked 
in everything around us. We can observe them in the 
street by looking at a building from different points of 
view, or by comparing the apparent sizes of the street 
lamps ; in the railway station, by watching the arriving 
or departing train ; and at sea, by noticing the vessels 
as they approach, or as they retire, ultimately vanish- 
ing from our sight in that line where the sea and sky 
appear to meet. 

All these interesting variations of appearance are 
in strict accordance with the laws of GEOMETRY and 
OPTICS. The former subject has been enlarged upon 
beginning with page 81 of this work, where a line, a 
point, an angle, etc., are defined ; other terms are 
explained at page 41 and the following pages ; to these 
we add a few definitions essential to the subject. 



A PLANE is a surface which is perfectly even and 
flat ; to use a familiar illustration, a plane is like the 
surface of a sheet of plate glass ; recollect particularly, 
that a surface which is at all curved, is not a plane. 

The GROUND=PLANE is the plane on which we 
stand ; the base-line is an imaginary line passing 




Fig. 299.— See page 255. 

through the middle of the feet as we stand square and 
erect ; and the vertical plane is supposed to stand 
on the base-line and perpendicular to it. 



250 



Hawkins^ Mechanical Drawing. 



Planes are parallel to each other when they are 
throughout their entire surfaces the same distance 
apart. 




^^^-.fl^UBEPUNt. 



Fig. 300. 

THE PERSPECTIVE PLANE is an upright square 
of glass, usually framed like a picture, with a base, so that 
it can stand up alone. This is placed between the eye 



of the spectator and the subject to be drawn, and as 
the drawing is sometimes made directly upon it, it is 
sometimes called the Picture or the Plane of the 
Picture. 




Fig. 301 



HORIZONTAL means perfectly level, like the sur- 
face of still water. We must be careful to understand 
perfectly the difference between the terms "level" and 
"even" or "flat." A surface may be even or fiat, 
without being level. Thus the wall is even and flat, 
but it is upright, not level ; level means a fixed, constant 
position. 



Hawkins' Mechanical Drawing. 



2sl 



In fig. 301 a house is shown in perspective in 
which the line 1/ L is the line of the horizon and VP 
is the, — 

VANISHING POINT.— The vanishing point is famil- 



t^i-iiW-^ 




Fig. 302. 

iarly represented by the rails on a trolley track on a 
straight road, which seem to approach each other in the 
distance, as shown in fig. 302 at V P. 

All parallel lines seen in perspective appear to meet 
in the same vanishing point. 



The value of the vanishing point may be seen in 
the view of a wooden house, fig. 303, where it {V P) 
gives direction to the retiring lines of the roof, side 
planks and door. 




Fig. 303- 

POINT OF SIGHT — This is that point in the eye 
where the lines or rays from the object cross each 
other, as shown at Pin fig. 305, also in fig. 299 at 5. 

VERTICAL means perfectly upright. If we attach 
a piece of thread to a weight, a small piece of lead for 



252 



Hawkins' Mechanical Drawing. 



example, and hold the thread with the lead hanging 
downwards, the thread will fall in an upright or verti- 
cal position. 

PARALLEL lines are said to be parallel to each 
other when they are throughout their whole lengths 
the same distance apart. 

PERPENDICULAR. "When one straight line, meet- 
ing another, makes the angles at the point of contact 
equal, each of the angles is called a right angle, and 
the lines are said to be perpendicular to each other. 
Remember especially that perpendicular and vertical 
have not the same meaning. Vertical means an un- 
varying upright position. Perpendicular means that 
one line or plane meets another line or plane at right 
angles. 

The fig. 295 on page 246 is a study in perspective, 
showing a water reflection. As rays from every visible 
part of the object are reflected, all following the same 
law, the reflection will appear to the eye inverted, and 
of the same size as the object. The arch itself forms 



the upper half of a hollow cylinder, and the reflection 
forms the lower half. The reflection shows much 
more of the interior of the arch than can be seen 
directly. The leaning tree, the boy fishing, and the 
receding banks, all are seen in accordance with the laws 
of reflection and perspective. 

THE HORIZONTAL LINE, THE POINT OF 
SIGHT AND THE VANISHING POINTS are the prin- 
cipal items. These should be studied in every room 
and during every walk, and the more pleasing accidents 
of form stored in the mind or committed to paper for 
future use. 

OPTICS, the science of sight, gives us the follow- 
ing laws : 

1. That we see by the agency of light. 

2. That light passes from objects to our eyes. 

3. That light travels in straight lines, which are 
called Visual Rays. 



Hawkins' Mechanical Drawing. 



253 




The human eye may be briefly described as a 
chamber of a spherical or globular form, with a circu- 
lar opening in front. This circular 
opening is called the pupil, and 
through it the visual rays pass to 
the interior of the eye. The visual 
rays, passing from space in all direc- 
* tions through the small pupil, are 

received upon what may be called the interior wall of 
the globular chamber forming the eye (see fig. 305). 
This interior wall is called the retina, and upon it the 
impressions of external objects are received, just as 
they are received upon a screen in a dark chamber. 
These impressions are conveyed by the optic nerve 
from the retina to the brain. 

In front of the pupil is a segment of a small 
sphere, composed of the cornea and the aqueous 
humor, both of which are transparent, and from their 
shape and density have a convergent effect upon the 
rays passing through them. 



Behind the pupil is the transparent crystalline lens, 
which, from its shape and its elasticity, is a powerful 
agent in aiding the convergence of the rays, and in 
bringing objects at various distances to a clear focus 
upon the retina. 



pft>0 




«tJ^ 



Fig- 305- 

The pupil has the power of contraction and dila- 
tion, which is influenced by the quantity of light enter- 
ing the eye, but when it is dilated to the utmost its 



^54 



Hawkins' Mechanical Drawing. 



size is very small in comparison with the great chamber 
forming the body of the eye. 

In fig. 305 we have a rough sectional diagram of 
the eye and an object in front of it. This object, an 
arrow, is seen by means of the visual rays proceeding 
from it, the principal two of which are shown. The 
visual ray from A passes through the pupil and is 
received upon the retina at a. In the same way the 
visual ray from B passes through the pupil and is 
received upon the retina at d. It will thus be seen 
that the impressions or images received upon the 
retina are inverted ; but, by long reason and expe- 
rience, the mind has acquired the habit of determining 
the real positions of objects, and does not, though 
the image is so received, imagine them to be upside 
down. 

It will also be observed, in the same way, that that 
portion of an object which is upon the right will be 
pictured upon the retina upon the left, and vice versa, 
but the mind, for the reasons before stated, never 



imagines the object to be reversed. This fact is 
another proof that, as mentioned at the commence- 
ment of our study, to see accurately is a matter of edu- 
cation and practice. 

And first of Optics ; it was asserted, page 252, that 
we see by the agency of light which passes from objects 
to our eyes in straight lines which are called Visual 
Rays. 

We see by the agency of light, as all objects, 
except such as may be styled self-luminous, when 
placed in a dark chamber are not perceivable by us, 
except by touch, smell or hearing ; we cannot see 
them ; they are invisible. But when, by removing a 
shutter or igniting a flame, we introduce something to 
the chamber which was not present when the chamber 
was dark, we become at once conscious of the appear- 
ance of the object, we perceive it by the sense of sight. 

This something which must always be present to 
enable us to see, is called Light ; all objects are made 
visible to the sense of seeing by its agency. 



i 



Hawkins' Mechanical Drawing. 



255 



Without light, natural or artificial, it would be 
impossible to distinguish one object from another. 




Fig. 306- 

That the Visual Rays pass from objects in straight 
lines to the eye may be proved by the following 
experiment (see fig. 306) : — Pierce two screens with a 



large pin, and place them so that the holes are in a 
straight line with a flame, as the light of a candle or 
lamp. On fixing the eye to one of these holes we are 
able to see the flame ; but if we slightly move the 
flame, one of the screens, or the eye, the flame is no 
longer visible. To be visible, the flame, the holes in 
the screens, and the eye must all be in the same straight 
line. See fig. 306. 

In fig. 299 the picture plane is represented by 
the rectangle IV X Y Z. Although the picture plane 
is here shown as a rectangle, it may be of any shape 
or of any size. 

The observer is at S, looking through the picture 
plane at the cross R C O II. The observer is standing 
upon a horizontal surface, which is called the ground 
plane. If we are in a room, the window may be called 
a picture plane and the floor a ground plane. 

The picture plane rests, as it were, upon the 
ground plane, in a line which passes ixom. Yto Z. The 



256 



Hawkins' Mechanical Drawing. 



two planes meet or intersect in this line, which is called 
the ground line. The ground line is sometimes called 
the picture line, or the measuring line. 

The visual rays, by means of which the observer 
sees the cross, will, in their course from it to the eye, 
pass through the picture plane. These visual rays will 
intersect the picture plane in a number of points, and 
if we mark the true positions of these points the result 
will be a perspective image of the cross. 



The rays are shown passing from the cross to the 
eye of the observer, and meeting the picture plane in 
points r, c, 0, h ; r being joined to 0, and c to h, we 
have the perspective image of the cross as it would 
appear to the observer at 5'. Of course an infinite 
number of rays proceed from the cross to the eye 
of the observer ; but it is quite evident that we need 
only consider those proceeding from the extremities of 
the object. 



Scale or approximate perspeetiv)e. 



Real, or true perspective, represents the object exactly as it is seen in nature, where the parts that are 
far away from the eye of the observer appear smaller than those nearby. Occasions arise, however, in practical 
life, with its numerous phases of industrial requirements, where the convenience of showing the complete form 
of the object in a single view might preferably be coupled with the convenience of scale dimensions. 



This has led to a modified perspective, that sacri- 
fices some of the accuracy in the appearance of the 
object to gain the advantage of scale dimensions; this 
form of perspective may be distinguished by the 
name — approximate or scale perspective — which does not 
represent the object exactly as seen in nature, but 
where those parts that are afar off are shown of the 
same size as those that are near by, and where the 
lines that run out into space are parallel to each other 
and do not converge into a vanishing point. 

To represent an object in perspective, the horizon 

and the point of vision will have to appear in the 
drawing as the fundamental starting points. 



Three dimensions are distinguished for the fixing 
of an object in space from a certain reference point. 
They are height, breadth and thickness, and are in 
their direction square to each other. The height is the 
fundamental direction, being derived from the direc- 
tion of gravity, that invariably extends to the center of 
the earth. 

All directions in the perspective determination of 
an object are parallel to these. 

Vertical lines and planes point toward the center 

of the earth, while horizontal planes, including the 

directions of breadth and thickness, are square to the 

vertical direction. In this, the principal visual ray 

extends in the direction of thickness. 
4 



257 



258 



Hawkins' Mechanical Drawing. 



For a clear understanding of perspective, it must be firmly fixed in mind, that for each prominent point of 
the object behind the picture plane, a corresponding point lies in the picture plane, in that position where a 
straight line or ray of sight that is going 
from the eye to the point of the object, 
cuts through the picture plane. 



Suppose we could replace these rays 
of sight by thin, visible threads of wire 
that would go through little holes in 
the picture plane, we could then walk 
around this bundle of rays, and by look- 
ing at it from three different directions, 
we would get three different views of 
it. We may look upon it from the top, 
from the side or from the end, where the 
bundle of rays all concentrate in the eye 
of the observer. 



Rom wYiSioH. 




End Yicw 



I'ig. 307. 



Figs. 307 and 308 show, in two cases, how these three views would appear. The end views are those where 
the perspective picture appears on the plane, while the top and side views only show where the rays intersect 
the picture plane. The top view shows how far, for example, point A is distant from a vertical line O Z, while 



Hawkins' Mechanical Drawing. 



259 



1 ftmfiwi Va>.>i. B.Y. _ JA Fw 




FtiinoFVisiM. 



SlDfYlEW. 
Gkouho Lwc. 



Edge of Rcturc fJANe. 




Fig. 308. 

the side view shows how far point A is below horizontal line O X, which is at the same height above the 
ground as the eye of the observer, O. Thus, all points of the cube can be located on the picture plane, and the 
outlines of the cube reproduced in perspective. 

Modified arrangements are shown in figs. 309 and 310 for parallel and angular perspective. 



26o 



Hawkins' Mechanical Drawing. 



The views are so arranged in relation to each other 
that the picture plane in the top view is parallel to the 
horizon and the ground-line, which latter is the inter- 
section of the picture plane with the level ground of 
the end or perspective view. At the same time the 




Z. TifVltW. 



Fig. 309. 

eye of the observer is in one and the same vertical line 
for both views, two vanishing points may be found in 



the horizon outside of the principal visual ray. To 
find the position of these two vanishing points in 



Top Yiftf. 




Fig. 310. 

the picture plane, the modified top view, fig.- 310, is 
used. 



Hawkins' Mechanical Drawing. 



261 



As all lines that end in a vanishing point must be 
parallel in reality, this parallelism may be seen in the 
top view and lines through the eye of the observer, 
parallel to the directions of the main lines of the object, 
will cut the picture plane at the vanishing points. 

Through these two vanishing points the directions 
of two sets of lines are found, the starting points of 
which are determined from the plane of measurement. 
The third set of lines, being vertical, also appears ver- 
tical and parallel in the picture. 

The position of each vertical line is found in the 
top view, where the light rays from the observing eye 
to the ends of the vertical lines intersect with the 
picture plane. Projecting these points down upon the 
rays to the vanishing points produces the vertical lines 
in the picture. 

For example, in fig. 3 1 1 , the purpose of perspective 
is entirely defeated by placing the eye of the observer 
directly in front of the object and arriving at the view 



taken in mechanical drawing which needs supplemen- 
tary views for complete comprehension of the form of 
the object. 




Fig- 311. 

In fig. 312 the eye of the observer is first placed di- 
rectly opposite the object, then it sees the object to the 
left but a short distance away, while in the third figure 



262 



Hawkins' Mechanical Drawing. 




Fig. 313. 



Hawkins' Mechanical Drawing. 



263 



£_M"VW 




£. lopYm. 



Fig. 312 (second patt). 



the observer is farther away from 
the object. In each case the 
picture plane and plane of meas- 
urement is at the front face of 
the cube. 

For such simple objects, it is 
not necessary to draw the top view 
at all. The only reminder of the 
top view is the eye or point of 
vision, the picture plane that falls 
together for the sake of conven- 
ience with the horizon of the end 
view and the ray that determines 
the measurement point J/, which 
is, in this suppressed reproduction, 
absolutely necessary, in order to 
find the apparent position of the 
real comers behind the picture 
plane. 



264 



Hawkins' Mechanical Drawing, 



So far, only square or sharp-cornered objects have 
been represented in perspective. 

It is evident, however, that round objects can also 
be shown in linear perspective, placing reference lines 
on the object and representing these as if they were real 
lines. A cylinder is thus shown in fig. 313 of which the 
end planes will appear very distinctly in sharp outlines. 

Vertically, only the outlines of the cylinder, as con- 
trasted against space, will appear as distinct outlines, 
while the reference lines will not appear and are there- 
fore shown only as dotted lines. 

Fig. 314 shows the approximate or scale perspective 
with all the axes drawn and the corresponding angles 
and scales marked. The outlines of the object running 
in these directions appear all parallel to the axes. 

The approximate or scale perspective completely 
avoids all the difficulties of choosing a point of sight, 
of having several views, vanishing points and measure- 
ment points, and thus offers a representative view, with 
a great saving of time and labor. Particularly for 
mechanical purposes, where an artistic impression is 
not called for, it presents a distinct advantage over the 
true or real perspective. 




».l'|v^.n,^i. j\;i" 



PicruRe R- AKf 

MEas. Pl. 




QgouKPt LiKC. 



Hawkins* Mechanical Drawing, 



265 





Fig. 314- 





^^E 




TABLES 

AND 

INDEX 


^^^^^^^^^^^^^^^^^^^^^H? 



268 



Hawkins' Mechanical Drawing, 




MARINERS' COMPASS. 



Useful Tables for Dpaugbtsmen. 



TABLE OF DECIMAL EQUIVALENTS. 

8ths, i6ths, 32ds and 64ths of an Inch. 



Sths. 


32nds. 


64tlis. 


Il=-5i5625 


i=-i25 


^=.03125 


^=.015625 


If =.546875 


i— 250 


A= -09375 


,\=. 046875 


Ii=-578i25 


1 =-375 


^=.15625 


^=.078125 


If =.609375 


5 =500 


A= -21875 


IT=- 109375 


|i=. 640625 


1=625 


A=-28l25 


^=.140625 


If =.671875 


l=.75o 


H=-34375 


H=-i7i875 


|f=. 703125 


1 =-875 


^=.40625 


4f=-203I25 


lf= -734375 


i6ths. 


il=-46875 


JfX. 234375 


If =.765625 


T«=o625 


H=-53i25 


H= -265625 


li=-796875 


A=-i875 


H=- 59375 


il =-296875 


If =.828125 


A=.3"5 


li= -65625 


Ii=-328i25 


l*= -859375 


tV=-437S 


11= -71875 


11= -35937.5 


|f=. 890625 


^=•5625 


11= .78125 


||=. 390625 


If =-921875 


ii=.6875 


H=-84375 


||=.42i875 


Ii=-953i25 


H=.8i25 


If =.90625 


||=.453i25 


fl=-984375 


il=-9375 


li=-96875 


H=. 484375 





269 



270 



Hawkins* Mechanical Drawing, 



TABLE OF DECiriAL EQUIVALENTS 
Of Millimeters and Fractions of Millimeters. 



mm. Inches. 


mm. Inches. 


mm. Inches. 


mm.. Inches. 


mm. Inchtt. 


bV=. 00079 


|g = . 01260 


§^=.02441 


If =.03622 


12= .47244 


A=-ooi57 


i5= -01339 


If =.02520 


|f=.o37oi 


13= .51181 


^=.00236 


JI=-oi4i7 


||=. 02598 


If =.03780 


14= .55118 


tV=-oo3I5 


ig=. 01496 


If =.02677 


|f=.03858 


15= .59055 


^=.00394 


fS=.oi575 


|f=.o2756 


1=03937 


16= .62992 


1^=. 00472 


|^=.oi654 


|f=.o2835 


2=.07S74 


17= .66929 


Tff=oo55i 


|f=.oi732 


|f=.029i3 


3=.ii8u 


18= .70866 


5^=. 00630 


||=.oi8ii 


If =.02992 


4=. 15748 


19= .74803 


/t=. 00709 


|^=. 01890 


If =.03071 


5=. 19685 


20= .78740 


iS=-oo787 


ff=.oi969 


I?=-O3i50 


6=. 23622 


21= .82677 


Ji=. 00866 


If =.02047 


|f=.03228 


7=.27559 


22= .86614 


if =.00945 


15 =.02 1 26 


|f=.03307 


8=.3i496 


23= .90551 


^=.01024 


|f = .02205 


|f-.o3386 


9=-35433 


24= .94488 


J|=.0II02 


ff = .02283 


|f=.03465 


io=.3937o 


25= .98425 


H=-oii8i 


|f=.02362 


ff=-03543 


1 1 =.43307 


26=1.02362 



10 mm. = I Centimeter = 0.3937 inches. 
10 cm. = I Decimeter = 3.937 " 
10 dm. = I Meter = 39.37 " 

25.4 mm. = I English Inch. 



Hawkins' Mechanical Drawing. 



271 



RULES RELATIVE TO THE CIRCLE. 

The circle contains a greater area than any other plane figure bounded by an equal perimeter or outline. 



TO FIND CIRCUMFERENCB — 

Multiply diameter by 3.1416. 
Or divide " " 0.3183. 



TO FIND DIAMETBR — 

Multiply circumference by 0.3183. 
Or divide " " 3.1416. 



To FIND RADIUS — 

Multiply circumference by 0.15915, 
Or divide " "6.28318. 



TO FIND SIDE OP AN INSCRIBED SQUARE- 

Multiply diameter by 0.7071. 

Or multiply circumference " 0.2251. 
Or divide " " 4.4428. 



TO FIND SIDE OF AN EQUAL SQUARE — 

Multiply diameter by 0.8862. 

Or divide " " 1.1284. 

Or multiply circumference " 0.2821. 
Or divide " " 3.545. 

SQUARE— 

A side multiplied by 1.4 142 equals diameter of its circumscribing circle. 

" " " 4.443 " circumference of its circumscribing circle. 

" " " 1.128 " diameter -i 

" " " 3.545 " circumference [• of an equal circle. 

" " " 1.273 " circle inches J 

TO FIND THE AREA OF A CIRCLE — 

Multiply circumference by one-quarter of the diameter. 
Or multiply the square of diameter by o. 7854. 

Or " " circumference " .07958. 

Or " " }i diameter " 3.1416. 



Contents of cylinder = area of end X length. Contents of wedge = area of base X }i altitude. Surface of cylinder = area of 
both ends X length X circumference. Surface of sphere = diameter squared X 31416, or = diameter X circumference. Contents of 
sphere = diameter cubed X .5236. Contents of pyramid or cone, right or oblique, regular or irregular = area of baise X l4 altitude. Area 
of triangle = base X /4 altitude. Area of parallelogram = base X altitude. Area of trapezoid = altitude X yi the sum of parallel sides. 



272 



Hawkins' Mechanical Drawing. 



ROMAN 


TABLE. 








I. denotes One. 


XVII. 


denotes Seventeen. 


II. 


11 


Two. 


XVIII. 




Eighteen. 


III. 


11 


Three. 


XIX. 




Nineteen. 


IV. 


ti 


Four. 


XX. 




Twenty. 


V. 


(1 


Five. 


XXX. 




Thirty. 


VI. 


(1 


Six. 


XL. 




Forty. 


VII. 


<< 


Seven. 


L. 




Fifty. 


VIIL 


ti 


Eight. 


LX. 




Sixty. 


IX. 


11 


Nine. 


LXX. 




Seventy, 


X. 


« 


Ten. 


LXXX. 




Eighty. 


XI. 


a 


Eleven. 


XC. 




Ninety. 


XII. 


(( 


Twelve, 


C. 




One hundred. 


XIII. 


a 


Thirteen. 


D. 




Five hundred. 


XIV. 


11 


Fourteen. 


M. 




One thousand, 


XV. 


a 


Fifteen. 


X. 




Ten thousand, 


XVI. 


« 


Sixteen. 


M. 




One million. 



50LID MEASURE, OR CUBIC HEASURE. 

This is used in measuring bodies, or things having 
length, breadth and height or depth. 

TABLE. 
1728 cubic inches (cu. in.) make i cubic foot (cu. ft.). 
27 cubic feet, " i cubic yard (cu. yd.). 

128 cubic feet, " i cord (C.). 



CIRCULAR MEASURE. 

60 seconds (") make i minute ('). 

60 minutes " i degree (°). 

360 degrees " i circum. (C.). 

The circumference of every circle whatever, is 
supposed to be divided into 360 equal parts, called 
degrees. 

A degree is ^^ of the circumference of any circle, 
small or large. 

A quadrant is a fourth of a circumference, or an 
arc of 90 degrees. 

A degree is divided into 60 parts called minutes, 
expressed by the sign ('), and each minute is divided 
into 60 seconds, expressed by (") ; so that the circum- 
ference of any circle contains 21,600 minutes, or 
1,296,000 seconds. 

LONG MEASURE— HEASURES OF LENGTH. 

12 inches = i foot. 40 rods = i furlong. 
3 feet = I yard. 8 furlongs = i common mile. 
5^ yards = i rod. 3 miles = i league. 

The mile (5,280 feetj of the above table is the 
legal mile of the United States and England, and is 
called the statute mile. 



Tables of Diameters, 
Qireumferenees and ^reas of Circles. 



Diam. 


Area. 


Circmn. 


Dlam. 


Area. 


Circum. 


Diam. 


Area. 


Circmn. 


Diam. 


Area. 


Circum. 


0.0 






2.0 


3.1416 


6.2833 


4.0 


12.5664 


12.5664 


6.0 


28.8743 


18.8496 


.1 


.007854 


.31416 


.1 


8.4636 


6.5973 


.1 


13.2025 


12.8805 


.1 


29.2247 


19.1637 


.2 


.031416 


.62833 


.2 


3.8013 


6.9115 


.2 


13.8544 


13.1947 


.2 


30.1907 


19.4779 


.8 


.070686 


.94248 


.3 


4.1548 


7.2257 


.8 


14.5220 


13.5088 


.8 


31.1725 


19.7920 


A 


.12566 


1.2566 


.4 


45239 


7.5398 


.4 


15.2053 


13.8230 


.4 


32.1699 


20.1063 


.6 


.19735 


1.5708 


.6 


4.9087 


7.8540 


.5 


15.9043 


14.1372 


.5 


83.1831 


20.4204 


.6 


.38274 


1.8850 


.6 


5.3093 


8.1681 


.6 


16.6190 


14.4513 


.6 


84.2119 


20.7345 


.7 


.38485 


2.1991 


.7 


5.7256 


8.4823 


.7 


17.3494 


14.7655 


.7 


35.2565 


21.0487 


.8 


.50266 


2.5133 


.8 


6.1575 


8.7965 


.8 


18.0956 


15.0796 


.8 


36.3168 


21.3628 


.9 


.63617 


2.8274 


,9 


6.6053 


9.1106 


.9 


18.8574 


15.3938 


.9 


37.3928 


21.6770 


1.0 


.7854 


3.1416 


3.0 


7.0686 


9.4248 


5.0 


19.6350 


15.7080 


7.0 


38.4845 


21.9911 


.1 


.9503 


3.4558 


.1 


7.5477 


9.7389 


.1 


20.4283 


16.0221 


.1 


39.5919 


23.3053 


.2 


1.1310 


3.7699 


.2 


8.0425 


10.0531 


.2 


21.2372 


16.3863 


.2 


40.7150 


23.6195 


.8 


1.3273 


4.0841 


.3 


8 5530 


10.3673 


.3 


22.0618 


16.6504 


.3 


41.8539 


23.9336 


.4 


1.5394 


4.3982 


.4 


9.0792 


10.6814 


.4 


23.9023 


16.9646 


.4 


43.0084 


23,2478 


.6 


1.7671 


4.7124 


.5 


9.6311 


10.9956 


.5 


23.7583 


17.2788 


.5 


44.1786 


23.5619 


.6 


2.0106 


5.0265 


.6 


10.1788 


11.3097 


.6 


24.6301 


17.5929 


.6 


45.3646 


23.8761 


.7 


2.2698 


5.3407 


.7 


10.7521 


11.6239 


.7 


25.5176 


17.9071 


.7 


46.5663 


24.1903 


.8 


2.5447 


5.6549 


.8 


11.3411 


11.9381 


.8 


26.4208 


18.2212 


.8 


47.7886 


24.5044 


.9 


2.8353 


5.9690 


.9 


11.9456 


13.2522 


.9 


27.3397 


18.5364 


.9 


49.0167 


24.8186 



273 



2 74 






Ha 


w kins' 


Mech 


anical Drawing 


» 






Diam. 


Area. 


Circum. 


Diam. 


Area. 


circum. 


Diam. 


Area. 


Circum. 


Diam. 


Area. 


Circum. 


8.0 


50.2655 


25.1327 


11.0 


95.0333 


34.5575 


14.0 


153.9380 


43.9823 


17.0 


236.9801 


53.4071 


.1 


51.5300 


25.4469 


.1 


96.7689 


34.8717 


.1 


156.1450 


44.2965 


.1 


229.6583 


53.7213 


.3 


52.8103 


25.7611 


.3 


98,5203 


85.1858 


.3 


158.3677 


44.6106 


.3 


232 3523 


54.0354 


.3 


54.1061 


26.0753 


.8 


100.2875 


85.5000 


.3 


160.6061 


44.9248 


.3 


235.0618 


54.3496 


.4 


55.4177 


26.3894 


A 


102.0703 


85.8143 


A 


163.8603 


45.2389 


.4 


237.7871 


54.6637 


.6 


66.7450 


26.7035 


.5 


103.8689 


36.1283 


.5 


165.1300 


45.5531 


.6 


240.^82 


54.9779 


.6 


58.0880 


27.0177 


.6 


105.6833 


36.4425 


.6 


167.4155 


45.8673 


.6 


243.3849 


55.2930 


.7 


59.4468 


27.8319 


.7 


107.5133 


36.7568 


.7 


169.7167 


46.1814 


.7 


246 0574 


65.6063 


.8 


60.8213 


27.6460 


.8 


109 3588 


37.0708 


.8 


173.0336 


46.4956 


.8 


248.8456 


55.9303 


.9 


62.2114 


27,9603 


.9 


111.3203 


37.3850 


.9 


174.3663 


46.8097 


.9 


251.6494 


56.3345 


9.0 


63.6173 


28.2743 


13.0 


113.0973 


87 6991 


15.0 


176.7146 


47.1239 


8.0 


254.4690 


66.5486 


.1 


65.0388 


28.5885 


.1 


114.9901 


88 0133 


.1 


179.0786 


47.4380 


.1 


257.3043 


56.8628 


.2 


66.4761 


28.9027 


.3 


116.8987 


3S. 3274 


.2 


181.4584 


47.7523 


.2 


260.1553 


67.1770 


.3 


67.9291 


29.2168 


.3 


118.8329 


88.6416 


.3 


183.8539 


48.0664 


.3 


263.0220 


57.4911 


.4 


69.3978 


29.5310 


.4 


130.7638 


38.9557 


.4 


186.2650 


48.3805 


.4 


265.9044 


57.8053 


.6 


70.8833 


29.8451 


.5 


122.7185 


89.2699 


.5 


188.6919 


48.6947 


.5 


268.8025 


58.1195 


.6 


72.3823 


30.1593 


.6 


124.6898 


39.5841 


.6 


191.1345 


49.0088 


.6 


271.7164 


68.4336 


.T 


73.8981 


30.4734 


.7 


126.6769 


39.0983 


.7 


193.5928 


49.3230 


.7 


274.6459 


58.7478 


.8 


75.4396 


30.7876 


.8 


128.6796 


40. 212 i 


.8 


196.0668 


49.6372 


.8 


277.5911 


69.0619 


.9 


76..9769 


81.1018 


.9 


130.6981 


40.6265 


.9 


198.5565 


49.9513 


.9 


280.5521 


59.3761 


iio.o 


78.5898 


31.4159 


13.0 


132.7323 


40 8407 


16.0 


201.0619 


50.2655 


19.0 


283.5287 


59.6903 


,1 


80.1185 


31.7301 


.1 


134.7823 


41.1549 


.1 


203.5831 


60.5796 


.1 


286.5211 


60.0044 


J8 


81.7128 


32.0443 


.3 


136.8478 


41-4690 


.2 


206.1199 


60.8938 


.3 


289.5293 


60.3186 


.8 


83.3229 


83.3584 


.3 


138.9291 


41.7833 


.3 


208.6724 


61.2080 


.3 


292.5530 


60.6327 


A 


84.9487 


82.6726 


.4 


141.0361 


42.0973 


.4 


211.2407 


61.5221 


.4 


235.5935 


60.9469 


.5 


86.5901 


82.9887 


.5 


143.1388 


42.4115 


.6 


213.8246 


51.8363 


.5 


298.6477 


61.3611 


is 


88.3473 


83.3009 


.6 


145.3673 


42.7257 


.6 


216.4243 


52.1504 


.6 


301.7186 


61.5752 


.7 


89.9203 


83.6150 


.7 


147.4114 


43.0398 


.7 


219.0397 


52.4646 


.7 


304.8053 


61.8894 


• • 

g 


91.6088 


33.9293 


.8 


149.5713 


43.3540 


.8 


221.6708 


62.7788 


.8 


807.9075 


62.2035 


.9 


93.3133 


84.2434 


.9 


151.7468 


48.6681 


.9 


224.3176 


53.0929 


.9 


811.0255 


63.5177 



.1 



Hawkins' Mechanical Drawing. 



275 



Diam. 


Area. 


Circum. 


Diam. 


Area. 


Circum. 


Diam. 


Area. 


Circum. 


Diam. 


Area. 


Circum. 


20.0 


3141593 


62.8319 


23.0 


415.4756 


72.2566 


26.0 


530.9392 


81.6814 


29,0 


660.5199 


91.1063 


.1 


817.3087 


68,1460 


.1 


419.0993 


72.5708 


.1 


535.0211 


81.9956 


.1 


665.0830 


91.4203 


.3 


320.4739 


63.4603 


.3 


422.7327 


72.8849 


.2 


539.12d7 


82.3097 


.2 


669.6619 


91.7345 


.3 


323.6547 


63.7743 


.3 


426.3848 


73.1991 


.3 


543.2521 


82.6339 


.3 


674.2565 


92.0487 


A 


326.8513 


64.0885 


.4 


430,0526 


73.5133 


.4 


547.3911 


82.9380 


.4 


678.8668 


92.3628 


.5 


330.0636 


64.4026 


.6 


433.7361 


73.8274 


.5 


551.5459 


83.3522 


.5 


683,4928 


92.6770 


.6 


333.2916 


64.7168 


.6 


437.4354 


74.1416 


.6 


555.7163 


83.5664 


.6 


688.1345 


92,9911 


.7 


3d6.5353 


65.0310 


.7 


441.1503 


74.4557 


.7 


559.9035 


83.8805 


.7 


692,7919 


03.3053 


.8 


339.7947 


65.3451 


.8 


444.8809 


74.7699 


.8 


564 1044 


84.1947 


.8 


697.4650 


93.6195 


.9 


343.0698 


65.6593 


.9 


448.6273 


75.0841 


.9 


668.3220 


84.5088 


.9 


702.1538 


93.9336 


21.0 


346.3606 


65.9734 


34.0 


452.3893 


75.3982 


27.0 


572.5553 


84.8230 


30.0 


706.8583 


94.2478 


.1 


349.6671 


66.2876 


.1 


456.1671 


75.7124 


.1 


576.8043 


85.1373 


.1 


711.5786 


94.5619 


_3 


353.9894 


66.6018 


.3 


459.9606 


76.0265 


.3 


581.0090 


85.4513 


.2 


716.3145 


94.8761 


'.9 


356.3273 


66.9159 


.3 


463.7698 


76.3407 


.3 


585.3494 


85.7655 


.3 


721.0663 


95,1903 


A 


359.6809 


67.2301 


.4 


467.5947 


76.6549 


.4 


589.6455 


86.0796 


.4 


725.8336 


95.5044 


.5 


363.0503 


67.5443 


.5 


471.4353 


76.9690 


.5 


593.9574 


86.3938 


.5 


730.6167 


95,8186 


.6 


866.4354 


67.8584 


.6 


475.2916 


77.2833 


.6 


598.2849 


86.7080 


.6 


735.4154 


96,13,37 


.7 


369.8361 


68.rt26 


.7 


459.1636 


77.5973 


.7 


602.6283 


87.0221 


o7 


740.2299 


96.4469 


.8 


373.2526 


68.4867 


.8 


483.0513 


77.9115 


.8 


606.9871 


87.3363 


.8 


745.0601 


96.7011 


.9 


876.6848 


68.8009 


.9 


486.9547 


78.3257 


.9 


611.3618 


87,6504 


.9 


749.9060 


97.0753 


22.0 


380.1327 


69.1150 


25.0 


490.8739 


78.5398 


28.0 


615.7532 


87.9646 


31.0 


754.7676 


97.3894 


.1 


383.5963 


69.4293 


.1 


494.8087 


78.8540 


.1 


630.1582 


88.2788 


.1 


759.6450 


97.7035 


.2 


387.07u6 


69.7434 


.2 


498.7593 


79.1681 


.3 


634.5800 


88.5929 


.2 


761.5380 


98.0177 


.3 


390.5707 


70.0575 


^ 


602.7355 


79.4823 


.3 


629.0175 


88.9071 


.3 


769.4467 


98.3319 


.4 


394.0814 


70.3717 


.4 


506.7075 


79.7965 


.4 


633.4707 


89.2213 


.4 


774.3713 


98.6460 


.5 


397.6078 


70.6858 


.5 


510.7053 


80.1106 


.5 


637.9397 


89.5354 


.5 


779.3113 


98.9603 


.6 


401.1500 


71.0000 


.6 


514.7185 


80.4248 


.6 


643.4243 


89.8495 


.6 


784.2672 


99.2743 


.7 


404.7078 


71.3142 


.7 


518.7476 


80.7389 


.7 


646.9246 


90.1637 


.7 


789.2388 


99.5885 


.8 


408.2814 


71.6283 


.8 


5227924 


81.0531 


.8 


651.4407 


90.4779 


.8 


794.2260 


99.9026 


.9 


411.8707 


71.9425 


.9 


526,8529 


81.3673 


.9 


655.9734 


90.7920 


.9 


799.2290 


100.2168 



276 



Hawkins' Mechanical Drawing, 



Diam. 


Area. 


Circnm. 


32.0 


804.2477 


f 100.5810 


.1 


809.2831 


100.8451 


.2 


814.3383 


101.1593 


.a 


819.3980 


101.4734 


.4 


834.4796 


101.7876 


.6 


829.5768 


102.1018 


.6 


834.6898 


102.4159 


.7 


839.8185 


102.7301 


.8 


844.9628 


103.0443 


.fl 


850.1229 


103.3584 


38.0 


855.2986 


103.6726 


.1 


860.4903 


103.9867 


.2 


865.6973 


104.3009 


.3 


870.9203 


104.6150 


.4 


876.1588 


104.9292 


.5 


881.4131 


105.2434 


.6 


888.6831 


105.5575 


.7 


891.9688 


105.8717 


.8 


897.2703 


106.1858 


.9 


802.5874 


106.5000 


84.0 


907.9203 


106.8143 


.1 


913.2688 


107.1283 


.3 


918.6331 


107.4425 


.3 


924.0131 


107.7566 


.4 


929.4088 


108.0708 


.5 


934.8202 


108.3849 


.6 


940.2473 


108.6991 


.7 


945.6901 


109.0133 


.8 


951.1486 


109.3274 


.9 


956.6228 


109.6410 



Diam. 



35.0 
.1 
.2 
.3 
.4 

.6 
.6 

.7 
.8 
.9 

36.0 
.1 
.2 
.3 
.4 

.5 
.6 

.7 
.8 
.9 

37.0 
.1 
.3 
.8 
;4 

.6 
.6 

.7 
.8 
.9 



Area. 



962.1128 
967.6184 
973.1397 
978.6768 
984.2296 

989.7980 

995.3823 

1000 9821 

1006.5977 

1012.3290 

1017.8760 
1023 5387 
1029.2172 
1034.9113 
1040.6212 

1046.3467 
1053.0880 
1057 8449 
1063.6176 
1069.4060 

1075.2101 
1081.0299 
1086.8654 
1093.7166 
1098.5835 

1104.4662 
1110.3645 
1116.2786 
1122.8083 
1128.1538 



Circnm. 



109.0557 
110.2699 
110.5841 
110.8983 
111.2124 

111.5265 
111.8407 
112.1549 
112.4690 
112.7832 

113.0973 
1U4115 
113.7257 
114.0398 
114.3540 

114.6681 
114.9823 
115.2965 
115.6106 
115.9248 

116.2389 
116.5531 
116.8672 
117.1814 
117.4956 

117.8097 
118.1339 
118.4380 
118.7522 
119.0664 



Diam. 



38.0 
.1 
.2 
.3 
.4 

.5 
.6 

.7 
.8 
.9 

89.0 
.1 
.2 
.3 

.4 

.5 
.6 

-7 
.8 
.9 

40.0 
.1 
.2 
.3 
.4 

.5 
.6 

.7 
.8 
.9 



Area. 



113^.1149 
1140.0918 
1146.0844 
1152.0927 
1158.1167 

1164.1564 
1170.2118 
1176.2830 
1183.3698 
1188.4724 

1194.5906 
1200.7246 
1206.8743 
1313.0396 
1319.3207 

1335.4175 
1231.6300 
1237.8583 
1344.1021 
1350.3617 

1256.6371 
1362.9381 
1269.2348 
1375.5573 
1381.8955 

1388.3493 
1894.3189 
1301.0043 
1307.4052 
1313.8219 



Clrcum. 



119.3805 
119.6947 
120.0088 
180.3230 
120.6372 

120.9513 
131.2655 
131.5796 
121.8938 
122.2080 

122.5331 
183.8363 
183.1504 
183.4648 
133.7788 

124.0929 
124.4071 
124.7213 
135.0354 
125.3495 

125.6637 
135.9779 
126.2920 
126.6063 
186.9203 

127.2345 

127.5487 
187.8688 
128.1770 
188.4911 



Diam. 



41.0 
.1 
.2 
.3 
.4 

,5 
.6 

.7 
.8 

.9 

42.0 
.1 
.2 
.3 
.4 

.5 
.6 
.7 
.8 
.9 

43.0 
.1 
.2 
.3 
.4 

.5 
.6 
.7 
.8 
.9 



Area. 



1320.2543 
1326.7024 
1333.1663 
1839.6458 
1346.14f0 

1352.6520 
1359.1786 
1365.7210 
1372.2791 
1378.8529 

1385.4424 
1392.0476 
1398.6685 
1405.3051 
1411.9574 

1418.6354 
1425.3092 
1433.0086 
1438.7338 
1445.4646 

1453.3012 
1458.9635 
1465.7415 
1478.5352 
1479.3446 

1486.1697 
1493.0105 
1499.8670 
1506.7393 
1513.6273 



Circnm. 



128.8053 
189.1195 
129.4336 
129.7478 
130.0619 

130.3761 
130.6903 
131.0044 
131.3186 
131.6227 

1319469 
132.3611 
138.5753 
138 8894 
133.^035 

133.5177 
133.8318 
134.1460 
134.4602 
134>774o 

135.0885 
135.4036 
135.7168 
136.0310 
136.3451 

136.6593 

136.9784 
137.8876 
137.6018 
1&7.9169 



Hawkins' Mechanical Drawing. 



277 



Diam. 


Area. 


Circum. 


Diam. 


Area. 


Circum. 


Diam. 


Area. 


Circum. 


Diam. 


Area. 


Circum. 


44.0 


1520.5308 


138.2301 


47.0 


1734.9445 


147.6550 


50.0 


1963,4954 


157,0796 


53.0 


2206.1834 


166.5044 


.1 


1527.4502 


138.5443 


.1 


1742.3351 


147.9690 


.1 


1971.8573 


157 3938 


.1 


2214.5165 


166.8186 


.2 


1534.3853 


138.8584 


.2 


1749.7414 


148.2833 


.3 


1979.3348 


157.7080 


.3 


2223.8653 


167 1327 


.3 


1541.3360 


139,1726 


.3 


1757.1635 


148 5973 


.3 


1987.1280 


158.0221 


.3 


2231.2298 


167.4469 


.4 


1548.3035 


139.4867 


.4 


1764.6012 


148.9115 


.4 


1995.0370 


158.3363 


.4 


2239.6100 


167.7610 


.5 


1555.2847 


139.8009 


.B 


1772.0546 


149.2257 


.5 


2003.9617 


158.6504 


.5 


2348.0059 


168.0752 


.6 


1563.3826 


140.1153 


.6 


1779.5237 


149.5398 


.6 


2010.9020 


158.9646 


.6 


3256.4175 


168.3894 


.7 


1569.2963 


140.4293 


.7 


1787.0086 


149.8540 


.7 


2018.8581 


159.3787 


.7 


3364.8448 


168 7035 


.8 


1576.3255 


140.7434 


.8 


1794.5091 


150.1681 


.8 


2026.8399 


159.5939 


.8 


3373.3879 


169.0177 


.9 


1583.3706 


141.0575 


.9 


1802.0254 


150.4823 


.9 


20348174 


159, 9071 


.9 


2281. "J 466 


169.3318 


45.0 


1590.4313 


141.3717 


48.0 


1809.5574 


150.7984 


51.0 


2042.0206 


16a2213 


54.0 


22902210 


169.6460 


.1 


1597.5077 


141.6858 


.1 


1817.1050 


151.1100 


.1 


2050.8395 


160.5354 


.1 


2298 7113 


169.9602 


.2 


1604.5999 


142. 0000 


.2 


1824.6684 


151.4248 


.3 


2058.8742 


160 8495 


.3 


2307.2171 


170 2743 


.3 


1611.7077 


143.3143 


.3 


1832.2475 


151.7389 


.3 


2066.9345 


161.1637 


.3 


2315.7386 


1705885 


A 


1618.8313 


142.6283 


.4 


1839.8423 


152,0531 


.4 


2074.9905 


161.4779 


.4 


2324.2759 


170.9026 


.5 


1625.9705 


143.9425 


.5 


1847.4528 


152.3673 


.5 


2083.0733 


161.7920 


.5 


2332.8289 


171 2168 


.6 


1633.1255 


143.2566 


.6 


1855.0790 


152.6814 


.6 


2091.1697 


163.1062 


.6 


2341 3976 


171,5310 


.7 


1640. 962 


143.5708 


.7 


1862.7210 


153.9956 


.7 


3099.2829 


162.4203 


.7 


2349.9830 


171.8451 


.8 


1647.4826 


143.8849 


.8 


1870.3786 


153.3097 


.8 


2107.4118 


162.7345 


8 


2858 5821 


172.1593 


.9 


1654.6847 


144.1991 


.9 


1878.0519 


153.6339 


.9 


2115^563 


163.0487 


.9 


3367.1979 


172.4735 


46.0 


1661 9025 


144.5133 


49.0 


1885.7409 


153.9380 


52.0 


2123.7166 


163.3628 


55.0 


2375.8394 


172.7876 


.1 


1669.1360 


144.8274 


.1 


1893.4457 


154.2533 


.1 


2131.8936 


163.6770 


.1 


2384.4767 


173.1017 


.2 


1676.3853 


145.1416 


r2. 


1901.1662 


154.5664 


.3 


3140.0843 


163.9911 


.3 


2393.1896 


173 4159 


.3 


1683.6502 


145.4557 

4 J ^ fV/l^/\ 


.3 


1908.9024 


154.8805 


.3 


2148-2917 


164.3053 


.3 


2401 8183 


173 7301 


.4 


1690.9308 


145.7699 


.4 


1916.6543 


155.1947 


.4 


2156 5149 


164.6195 


.4 


2410.5126 


174.0442 


.5 


1698.2273 


146.0841 


.5 


1924.4218 


155.5088 


,5 


2164.7537 


164.9336 


.5 


2419.2327 


1743584 


.6 


1705.5392 


146.3983 


.6 


1932.2051 


155.8330 


.6 


2173.0082 


165.3479 


6 


2427.9485 


174.6726 


.7 


1713.8670 


146.7124 


.7 


1940.0042 


156.1373 


.7 


2181.2785 


165.5619 


.7 


2436 6899 


174 9867 


.8 


1720.2105 


147.0265 

M Art f\ 1 rifv 


.8 


1947.8189 


156.4513 


.8 


2189.5644 


165.8761 


8 


2145.4471 


175.3009 


.9 


1727.5697 


147.3407 


, ,9 


1955.6493 


156.7655 


.9 


2197.8661 


166.1903 


.9 


2454.2200 


175.6150 



2 78 



Hawkins' Mechanical Drawing. 

UNITED STATES STANDARD SIZES OF WROUOHT IRON WELDED PIPE. 



Inside 

diameter 

noiD. 


Actual 

outside 

Diameter. 


Thick- 
Bess. 


Actual 

Inside 

Diameter. 


External 
circum- 
ference. 


Internal 
clrcam- 
ferencj. 


Length of 
pipe per 
square' 
foot of 
outside 
surface 


Length of 
pipe per 
square 
loot of 
Inside 
surface. 


Kfternal 
area, 


Actual 

totornal 

ares. 


Length of 
pipe con- 
taining 
one 

cubic fJOt. 


Weight 

per foot 

or length. 


No. of 
threads 
per Inch 
of ecrow. 


Length 
perfect 
screw 


1 


'.405 


'.068 


0.269 


1.272 


0.848 


9.440 


14.15 


.129 


,0572 


2500. 


.243 


27 


0.19 


4 


.54 


.088 


0.364 


1.696 


1.144 


7.075 


10.50 


.229 


.1041 


1385. 


.422 


18 


0.29 


i 


.675 


.091 


0.493 


2.121 


1.552 


5.657 


7.67 ■ 


.358 


.1916 


751.5 


.561 


18 


0.30 


i 


.840 


.109 


0.622 


2.652 


1.957 


4,502 


6.13 


.554 


.3048 


472.4 


.845 


14 


0,39 


'i 


1.050 


,113 


0.824 


3.299 


2.589 


3.637 


4.635 


.866 


.5333 


270.0. 


1.126 


14 


0.40 


1 


1.315 


.134 


1.047 


4.134 


3.292 


2.903 


3.679 


1.357 


.8627 


166.9 


1.670 


IH 


0.51 


U 


1.660 


.140 


1.38 


5.215 


4,335 


2.301 


2.768 


2.164 


1.496 


96.25 


2.258 


Hi 


0.54 


li 


1.90 


,145 


1.61 


5.969 


5.061 


2.010 


2.371 


2.835 


2.038 


70.65 


2.694 


IH 


0.55 


2 


2.S75 


.154 


2.067 


7.461 


6.494 


1.611 


1.848 


4.430 


3-355 


42.36 


3.667 


lU 


0.58 


2i 


2.875 


.204 


2.467 


9.032 


7.754 


1.328 


1.547 


6.491 


4.783 


30.11 


5.773 


8 


0.89 


3 


3.50 


.217 


3.066 


10.998 


9.636 


1.091 


1. 245 


9.621 


7.388 


19.40 


7.547 


8 


0.95 


3} 


4.0 


.226 


3.548 


12.566 


11.146 


.9.55 


1.077 


12.566 


9.837 


14.56 


9.055 


8 


1.00 


14 


4.50 


.237 


4.026 


14.137 


12.648 


.849 


0.949 


15.904 


12.730 


11.31 


10.728 


8 


1.05 


'4i 


5.0 


.247 


4.506 


15.708 


14.153 


765 


0.848 


^9.635 


15.939 


9.03 


12.492 


8 


1.10 


5 


6.563 


,259 


5.045 


1-7.475 


15.849 


629 


0.757 


24.299 


19.990 


7.20 


14.564 


8 


1.16 


6 


6.625 


.280 


5,065 


20.813 


19.054 


.577 


0.630 


.34.471 


28.889 


4.98 


18.767 


8 


1.26 


7 


7.625 


.301 


7;023 


23,954 


22,063 


.505 


0.544 


45.663 


38.727 


3.72 


23.410 


8 


1.36 


8 


8.625 


.322 


7.981 


27.096 


25.076 


.444 


0.478 


58.426 


50.039 


2.88 


28.348 


8 


1,46 


9 


9.688 


.344 


9.00 


30.433 


28.277 


.394 


a425 


73.716 


63-633 


2.26 


34.677 


8 


1.67 


10 


10.750 


.366 


10.018 


33.772 


31.475 


.355 


0,381 


90.762 


78.838 


1.80 


40.641' 


8 


1.68 



Thread taper three-fourths inch to one foot. 

All pipe below i^ inches is butt-welded, and proved to 300 pounds per square inch ; 1% inch and above is lap-welded and ■proved 
to 500 pounds per square inch. 



u 

< 
H 

01 -g 
H a 

§ i 



H 


as 


Z 


«J 




a 


0} 


E 


7: 


S 




Q 


<o 


p 


u 




o 


en 


3 


« 


< 


N 


o 


tfj 


cu 


^ 


c^ 


Ol 



^ I 



Qi 

O 

u. 

CO 

a 

< 

a 
z 
< 



c 
e 



Hawkins* Mechanical Drawing, 



279 






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28o 



Hawkins' Mechanical Drawing. 



UNITED STATES STANDARD SIZES OF BOLTS. 



DIAMETER, 


distance 
Across Flats, 


Distance 
Across Corners, 


Thickness 




SCDARK AND Hex 


HEX. 


OF Head. 


X" 


y^" 


9 " 
TS 


X" 


H 


H 


H 


H 


'A 


% 


1 


tV 


y^ 


1^ 


1^ 


H 


Va 


1^ 


lA 


/8 


H 


lA 


m 


H 


1 


15/a 


1/8 


H 


i^ 


m 


2A 


M 


H 


2 


2A 


1 


m 


2tV 


2>^ 


lA 


IK 


23/8 


2% 


lA 


if^ 


2.^ 


^H 


lA 


1^ 


23^ 


3A 


1/8 


1/8 


2|| 


3H 


m 


2 


3)4 


3/8 


h% 


vx 


sy. 


4tV 


1^ 


2% 


Sji 


4>^ 


M-l 


2K 


4X 


4^ 


2>€ 


3 


45/8 


■^H 


2A 



UNITED STATES STANDARD SCREW 
THREAD GAUGE. 




Kg. 316. 



Some Things Personal. 



In the preparation of this work the idea of self-help has never been forgotten; 
nothing has been held back or omitted which would, in the author's opinion, tend 
to advance the student in the draughtsman's art. 

The volume contains the experience in practical drawing, as related to engineering 
and mechanics, of over one hundred years, i. e., the author's, fir. Perrott's and Mr. Lucas' 
experiences added together exceed that period. 

Hence, the work should be really helpful ; it has been aimed also to be enter- 
taining and with easy tasks; all the illustrations of the book are recommended as 
models for practice— they have been selected with that view. 

Moreover, as between author and publishers, the latter have agreed to issue the 
work in the most thorough style possible— as to paper, printing and binding — and to 
sell it at a very generously low price, considering all things. 

With the closing words "hail and farewell," the author bids adieu (Qod be with 
you) to the reader and the student. 

281 



282 



Hawkins' Mechanical Drawing. 




BSACON UGRV. 



^awl^ins' ||}p TVl^^f^^"!^^^ l^rawing. 



Jndex. 



PAGE 

Acute Angle, def 42 

Acute-Angled Triangle, def 50 

Addendum Circle, illas 200 

Alphabets, Gothic, desc 171 

Altitude, def 41 

Altitude of a Polygon, def 47 

American Machinist, Quotation from 141 

Angle, def 41, 83 



To bisect an.., 
To draw an.. . 

Angle-Iron, illus. . 

Angle-Plate, illus.. 



89 
89 
75 
75 



Angular Perspective Drawing, illus 260, 265 

Apex, def 42 

Apex of an Angle, def 42 

Arc, def. 42 

Complement of an 99 

Cosecant of an 99 

Cotangent of an 99 

Sine of an 99 

Supplement of an 99 

Tangent of an 99 

Versed Sine of an 99 

Arc of Circle, To find the center of an 90 



283 



284 Hawkins' Mecb 

PACE 

Arcs, Drawing 146 

Ulus 146 

Xrrow^-Heads, liow made 172, 176 

Axiom, def. 83 

Axis, Conjugate, def. 96 

Of a Figure, def 43 

Of a Solid, def 42 

TratkSverse, def. 96 

Backlash in Oearing 215 

Bacl(vpard Projection desc. 152, illus. 152-3 

Base, def 43 

Of a Polygon, def 47 

Beacon Liglit, illus 282 

Beam €ompasses desc. 124, illus. 124 

Bendingr Macliine, Hydraulic desc. 221, illus. 220-1 

Benjamin, Prof. Clias., " How and What to Study ".. 23 

Bevei-Gear, desc 201 

Bevel Mortise Wiieel, desc 203 

Bevel Wheel, desc. 199, illus. 203 

Bisect, def , 43 



anical Drawing. 

PA.OB 

Bisector, def. 43 

Blackboard, illus. and desc 27 

Blackboard Branding 28 

Blue Printings desc. 186, illus. 187 

Test pieces 188 

Blue Prints, Office rules for 196 

Black Process Copying 188 

Boiler-PIate, Riveted, illus 76 

Bolt, Square-head, illus 76 

Bolt and Nut, Square-head desc. 144, illus. 145 

Hexagon desc. 144, illus. 76, 144 

Bow-Dividers desc. 123, illus. 122 

Bow-Pencil, desc , 123 

Bows, Use of. 242 

Brick, Section-Lining, illus 182 

Broken Lines, How to Draw 33 

Def 46 

Bumping Post, illus 226 

Calipers, illus vi 

Cast-iron, Section-Lining, illus 182 



Hawkins' Mechanical Drawing. 



285 



Canlking Tool, illus 76 

Center L.Ine, def 46 

Center Lilnes, In Drawings 240-1 

In Shop Drawings 192 

Ctaalk-Crayon desc. 27, illus. 27, 37 

Cbalk-TFork 27 

Instruments for Drawing, illus 29 

Ctaannel-Iron, illus 75 

Checking Dravrings 194 

Circle, def 100, 43 

To describe about a square 93 

about a triangle 93 

through two points 90 

through three points 90 

To find the center ." 90 

To inscribe in a square 94 

in a triangle 94 

Circles, Drawing desa 146, illus. 146 

Circumference of a Circle 43 

Circomscribe, def 43 

Circular Pitcli Line, illus 300 



Classifying Drawings, Office Rules for. 

Clearance in TFheel Teetli 

Cog-^Vlieel def. 201, illus, 

Section- Lining, illus 

Coin, Perspective View of a, illus 

Color and Tints 

Compass, Mariners', illus 

Compasses, Beam, desc. and illus 

Desc. and illus 

For holding chalk, illus 

How to hold, illus 

Complement of an Arc 

Composition, Section-Lining, illus. 

ConcaTC, def. 

Cone, def 

Conjugate Axis, def. 

Construction, def 

Line, def 

Contents, Table of 

Contour, def - 



Convergence, def. 



PAGE 
191 

201 

248 
185 
268 
124 
121 
29 
136 

99 
182 

44 
44 
96 

44 
46 

24 
44 
44' 



286 Hawkins* Mecb 

PAGE 

Convex, def 44 

Copying Dranrlni^s, Black Process 188 

Blueprinting 186 

Tracing 184 

Copyright vii 

Corner, def 44 

Corollary, def 83 

Co-secant of an Arc, def 99 

Co-sine of an Arc, def 99 

Co-tangent of an Arc, def 99 

Crane, desc 219 

Working drawing of, illus 218 

Cross-Hatches, def 44 

Cross-hatching Draw^ings 182 

Crown Wheel, illus 208 

Curve, def 44 

Carved Line, def 46 

Curved Lines, Drawing, desc 69 

Drawing Figures of 70, 72, 73 

How to Draw 35 

Illus 70 



anical Drawing, 

FAOB 

Curved §urface, def 49 

Curve or Scroll, illus 117 

Cut Gears, desc 215 

Cylinder, def 44 

' Cylindrical, def 44 

Cylindrical Projection, illus 161 

Dash liine, def 46 

Decimal Equivalents, Table of 269 

Dedication ix 

Definitions, Preliminary 41 

Degree, def 4i| 44 

Describe, def 44 

Design, def. , 44 

Symmetry in, def 50 

Designing Oears 209 

Detail Draivings, Office Rules for 191 

Develop, def 45 

Diagonal, def 45 

Diagonals of a Polygon, def 47 

Diameter, def. 45 



Hawkins* Mech 

PAGE 

Diameter, Of a Circle 43 

Diameters of ivneels, How to Measure 199 

Diametral Pitch, desc. 200 

Of Gears 212 

Dimensioning^ Dranrings desc. 176, illus. 177, 179 

Dimension Line, def. 46 

Dimensions on Dravrings, Office Rttles for 192 

Dividers and Compasses, desc 119 

Dividers, illus 82, 119 

Bisecting, desc 119 

Bow, illus 122 

' ' Point " 242 

Proportional desc. 119, Ulns. 120 

Spring Bow, desc 124 

Dodecahedron, def 48 

Dot-and-Dash Line, def. 46 

Dotted Line, def 46 

Draaghtsmen, Useful Tables for 269-280 

Dranring, Blackboard 28 

Free-hand 55 

Linear Perspective 247 



anical Drawing. 287 

PAOK 

Drawing, Parallel Perspective 260-1 

Projection, desc 148 

Scale Perspective 257 

Spur Gear, illus 163, 211 

Spur Wheel, desc 162 

Straight Line Figiares desc. 65, illus. 66-7-8 

Symbols 193 

The Pitch Line 209 

To Scale, desc 126 

Working, def. 51 

Dra'wing-Board desc. 107, iUus. 102, 106, 108 

Expansion and Contraction of 108 

How to Construct 107 

Trestles, illus no, in 

Draining Instruments, desc 103 

How to Select 104 

nius 105 

Outfit Recommended 104 

Drawing Materials, desc 103 

Drawing Office Rules 191 

Dranring Paper, desc 132 



288 Hawkins' Meeb 

PAQB 

Dravring Paper, Erasing Lines 140 

Fixing of, illus 102 

Fixing on the Board 139 

Pasting 184 

" Points " 243 

Patent Office Sizes 234 

Sizes of. 133 

l>ra\i^ing Pencils, desc. and illus 118 

How to Use 56 

Dra'wing; Pen, Filling with ink, illus 130 

Dravring Pens, desc. and illus 129 

Drawing-Pins, desc no 

DraAving Scales, desc 126 

Draw^ings, Cleaning, desc 169 

Color and Finish, note 185 

Dimensioning, desc 176 

Inking in, desc 167 

Lettering, desc 171 

Patent Office Rules for 233 

Reproducing 186 

Section-Lining, desc 182 



anical Drawing. 

FAGE 

Drawings, Shading desc. 180, illus. 180,225 

Size of, Office Rules , 191 

Tint and Color, desc 184 

Dramring-Table, desc... in 

Folding Legs, illus 104 

Edge, def 45 

Elevation, def 45 

Elevation and Section, Spur Wheel, .desc. 216, illus. 212 

Ellipse, An, desc 96, 118 

To describe when length and breadth are given 96 

Envelopes, Portfolio, desc 142 

Equiangular Triangle, def 45 

Equilateral Triangle, def. 50 

Erasing, " Points "on 242 

Eye, illus. and desc 253 

Effect of Light on 253 

Face, def 45 

Faced Surfaces, Points, etc 242 

Figures, Drawing Straight-line 65 



Hawkins' Mecb 

PAGB 

Flffures, Numerals, examples of i73 

Straight-line, illas 66 

File Handle, desc. and illus 144 

Finger and Thumb Liines, illus 64 

Finislied Surfaces, How to indicate 193 

"Points" 242 

Finishing, def 45 

Flanged-tooth WTieel, desc 205 

Flat Pattern, def. 47 

Foreshortening, def 45 

Forward Projection desc. 151, 152, illus. 155 

Free-hand, def. 45 

Free-hand Drawing ^ 55.78 

First Lesson in 30 

Penciling, illus. 54 

Free-hand Illustration, a Water Wheel 78 

Friction-Clutch and Pulley, desc 224 

Friction Oear-T¥heels, desc 201 

Full Line, def. 46 



anical Drawing. 289 

PAGE 

Gear, def i99 

Oearing, desc i99 

Drawing desc. 162, illus. 163 

Gearing and Design 197 

Gears, A Train of, desc 208 

Speed of. 208 

Gear-WTieels, Spur, illus 198 

Generated, def 45 

Geometric, def 45 

Geometrical Axioms 84 

Geometrical Draw^ing, desc 81 

Problems in 86 

Geometrical Signs 84 

Geometry, defs 249 

Elements of 81 

Gothic Letters, illus 173 

Grooved Friction TFheels, desc 201 

Ground-Plane def. 249, 255, illus. 249 

Half-Tint, def. 45 

Hand-^Vlieel, iUus 77 



290 Hawkins' Mech 

PAOK 

Sang:er, illus 179 

Helical TV^heel desc. 199, illus. 207 

Hemisphere, def 45 

Heptagon, def. 47 

Hexagon, def 47 

To Construct a 95 

Hexagon-Head Bolt, illus 144 

Hexahedron, def. 48 

Horizontal, def 45, 250 

Horizontal Une, in Drawing, illus 250 

How to Draw 32 

In Perspective 252 

Hypothesis, def. 83 

Icosahedron, def. 48 

India Ink, desc. and illus 131 

Dish or Tile, illus 131 

India Rubber Eraser, illus 132 

Use of. 240 

Ink, Preparing, for Drawings, desc 167 

Test for Good, desc 167 



anical Drawing. 

VA«B 

Ink Eraser, Steel, desc. and illus. 132 

Inking, illus 166, 169 

Long Lines, illus 170 

Rules of Procedure 168 

Short Work, illus ; 169 

" Inking in " Drawings, desc 167 

' ' Points," etc 239, 243 

Patent Office Drawings 234 

Inscribe, def 45 

Instrumental, def. 45 

Instruments for Chalk-work, illus 29 

Internal Gear, desc 201 

Internal-Gear liHieel, illus 207 

Introduction 15 

Isosceles Triangle, def 50 

Lantern-'Wheel, desc 201 

liathe-Dog, illus 76 

Lemma, def 83 

liCttering, Blow-Off Valve, illas 175 

Drawings, desc 171 



Hawkins' Mecb 

PAOB 

lilght) and Sense of Seeing 354 

Bxperiment with, illns 255 

Laws of 252 

Line, def 82 

To Divide into Equal Parts 89 

Linear Perspective Dranring 247 

lilnes, def 45 

Note 65 

Parallel, def 83 

Link motion, Stephenson's, illus 225 

Longitudinal, def 46 

Lucas, Theo., Acknowledgement 23, 266 

Marking measurements on Drawings 243 

Rleetaanleai Dra%ving 137, 247 

Elevation 138 

Examples . 143 

Procedure 141 

ninerra, Free-hand Sketch of iii 

niter- Wbeel desc. 199, 204, illus. 204 

Model, def. 46 



anieal Drawing, 



391 



Nonagon, def 47 

Numbering Drawings, Office Rules for 194-5 

Numerals, illus 173 

Oblique, def. 46 

Oblique Lines How to Draw, 32, 58, illus. 59, 63 

Oblong, def. 46 

Obtuse Angle, def. 42 

Obtuse- Angled Triangle, def. 50 

Octahedron, def 48 

Octagon, def. 47 

To Describe on a gjiven straight line 95 

To Inscribe in a circle 96 

Oil Can, illus 77 

Optic Nerve, illus 253 

Optics, in Drawing, def 252 

Outline Picture, desc 152 

Oral, def 46 

How to Draw an 71 

Overall, def 46 



292 Hawkins' Mech 

rAGB 

Paper, Fastening Drawing on 184 

Rule or Scale 242 

Sensitized, desc 188 

The Right Side ot 241 

Parallel, def. 46 

Parallel Liines, def 83, 252 

To Draw 88 

In Perspective 251 

Parallel Perspective Draining, illus 260 to 263 

Parallel Rule desc. 115, illus. 114-5 

Parallelogram, def 47 

To Construct 93 

Pasting Dratving Paper, " Points " 243 

Patent Office Drawings 235, illus. 236 

Rules of Great Britain 336 

Rules of U. S. 233 

Patterns, def. 46 

Numbering, from drawings 194 

Pedestal, illus 178-9 

Pen, Hand holding, illus 166, 169, 170 

Pencil, Function of a 142 



anical Drawing. 

PASS 

Pencil, How to Cut, illus 57 

How to Hold, illus 54, 59, 60 

How to Use 56 

Pencil-Compasses, desc 143 

How to Hold 143 

Penciling, desc. and illus 139 

" Points" 143, 240 

Pencil Lines, How to Make 119 

Pencils, Sharpening Points of 143, 241 

Penknife, illus 52 

Pens, Drawing, illus 129 

Lettering and Figuring, illus 172 

Pentagon, def. 47 

To Inscribe in a circle 94 

Perimeter, def. 47 

Of a Polygon, def 47 

Periphery of a IVbeel, def 200 

Perpendicular, def 47, 252 

Perpendicular Lines, How to Draw 31, 61, 62 

Perrott, Oeo., Acknowledgement 23, 266 

Personal, Note from the Author 366 



Hawkins' Mecb 

PAGK 

Perspective Drawings def. 47, illus. 250 

Definitions of Terms used in 249 

Geometrical Terms used in 248 

Of a Bridge, illus 249 

Scale or Approximate 257 

Vanishing Point, illus 251 

Water Reflection, illus 246 

Per§pective, Linear, def 247 

Perspective Plane, def. 250 

Picture Plane, desc 255 

In Drawing, illus .249, 250 

In Perspective, illus 258 

Plnlon-'Wlieel, desc 201 

Piston Rod, desc 223 

PItcli Circle in Gearing 200 

Pitch Line, Drawing the 209 

In Gearing 200 

Plan, def ■. 47 

Plan of tlie Work 21 

Plane, iu Perspective, def. 249 

Plane of tlic Picture, def 250 



anical Drawing. 293 

PAGE 

Plane Surface, def. ^g 

Point, def S2 

Point of Sig^bt, in Perspective Drawing 251 

Points, relating to Chalk Drawings 36 

To be observed in Sketching 141-2 

Useful Hints and 170, 239 

Polygon, def , 47 

Polyhedron, def ^g 

Postulate, def 83 

Pounce, How to Use, desc 170, 186 

Preface 13 

Preparatory Practice in Drawing 30 

Prism, def 49 

Problems, def 83 

Geometrical 86 

Produce, def 49 

Profile, def 49 

Projection, Backward, illus 153-4 

Def 49 

Cylindrical Outline, desc 159 

Cylindrical Surface, illus 161 



294 



Hawkins' Mecb 



Projection, Forward desc. 152, illus. 155 

Hexagon Nut, illns 160 

Marking Dimensions 150 

Lines of Sight iSo 

Scaling and Measuring in 149 

Sight-Lines, illus 151 

Sloping Surface, desc i59 

Spur-Wheel, desc 162 

Projection Dra\ring, desc 148 

Illus 149, 151, 153, 154, 155. 157, 158, 160, 161, 163 

Principles of 148 

Spur-Wheel, illus 163, 212 

Proportional Dividers, illus 120 

Proportions of Teeth of Wheels 210 

Proposition, def 83 

Protractor, desc..' 128 

Pulley and Friction Clatcta, illus 224 

Punchinv Press illus. 222, desc. 223 



Quadrant, def 

^Quadrilateral, def., 
<|nadri8ect, def 



49 
47 
49 



anical Drawing. 

Rack and Pinion, desc 305 

Radius of a Circle 43 

Reading; l¥orking; Drawings, desc 329 

Rectangle, def 48 

To Construct a 92 

Reproducing Dranvings, desc... 186 

Reverse Curve, def 44 

Rhomboid, def 48 

Rhombus, def. 48 

Right- Angle, def 42 

Triangle, def 50 

Robinson, A. "W., W. E., note. Office Rules 191 

Rolling-Circle in Gear- Wheel 200 

Rule, Area of a Circle, To find the 271 

Circumference of a Circle, To find the 271 

Cylinder, To find the contents of a 271 v 

Diameter of a Circle, To find the 271 

Illus 82 

Inscribed Square, To find side of an 271 

Parallelogram, To find the area of a 271 

Pyramid or Cone, To find the contents of a ajx 



Hawkins' Mecba 

PAGE 

Rule, Radios of a circle. To find the 271 

Sphere, To find the contents of a 271 

Square, To find the side of an equal 271 

Trapezoid, To find the area of a 271 

Triangle, To find the area of a 271 

Two-foot desc., 127, 128, lUus. 128 

Wedge, To find the contents of a 271 

Rules for Drawing Office 191 

Wheels, To find proportions of. 219 

Sand Paper, Removing surface of paper 168 

Scale, Drawing to, desc 126 

Scale DraTTingg, To read 230 

Scale, Flat, illus 127 

Triangular, illus 127 

Scalene Triangle, def 50 

Scale or Approximate Perspective 257 

Scale Rnle, for Proportions of Teeth 214 

Scales, Drawing, desc 126 

Scboliam, def. 83 

Screw-Tliread, U. S. Standard Gauge 280 



nical Drawing. 295 

PAGB 

Scroll or Curve, desc 117 

Universal Curve, illus 134 

Secant of an Arc 99 

Section, def 49 

Drawing iUus. 163, desc. 160 

Sectional, def 49 

Section-Liner, iUus 116 

Section Liines in Drawings 240 

Section-Lilningr, Cast-iron, etc. , illus 182 

Cog- Wheel, illus 183 

Section-Lining Drawings desc. 182, nias. 183 

Wheel Hub, nius 184 

Selecting Drawing Instruments 103, 240 

Semi-Circle, def 43 

Sensitized Paper, desc 188 

Set-Square, illus 102, 114 

Shading Curves, illus 181 

Shading Drawings 180 

Shadoiv, def 49 

Sbado w^ Line, def 46 

Shadow^ LJnes, " Points " 241 



296 Hawkins' Mecb 

PAGB 

Sharpening Pencils 57 

Shop Dra^vings, Office Rules 192 

Sig^ht, Point of, in Perspective Drawing 252 

Sense of 254 

Sight Lines in Projection, illus 157 

Sine of an Arc 99 

Sice^v-G earing, dese 203 

Sli.etch Books, desc 142 

Office Practice 194 

Slietches, details 142 

Slcetch, Free-hand, Advantage of 55 

Sicetching desc. 141, note 17 

Points to be observed in 141-2 

Sloping Surface in Projection desc. 159, illus. 166 

Solid, def 49, 83 

Solid Pattern, def 47 

Speed of Gears 208 

Sphere, def. 49 

Spiral Curve, def. 44 

Spring Bows.. ., illus. 122, 123, desc. 124 

Spur-Gear desc. 201, illus. 211 



anical Drawing. 

PAGB 

Spur mortise- Wheel, illus 202 

Spur-AVheel, desc 199, 216 

How to Draw 209 

Illus 198 

Projection desc. 162, illus. 163 

Teeth of cast-iron, desc . 202 

Square, def 48 

To Convert into an Octagon 95 

To Describe about a Circle 94 

To Inscribe in a Circle 93 

Standards, for U. S 278 

Office Rules for 193 

Steady Rest, Scale, illus 228 

Straight Line, def. 46 

To Draw a Perpendicular to a 86 

Drawing Figures of 66-7-8 

How to Draw a 57> 59 

To Bisect a , 86 

Steel, Section-I^ining, illus . . , 182 

Steel Gears, Economy of 216 

Surface, def. 49, 82 

Symbols, representing Materials 193 



Hawkins' Mecb 

PAGE 

Table of Areas of Circles 273 — 277 

Bolts, Standard Sizes of. 280 

Circular Measure 272 

Circumferences of Circles 273 — 277 

Contents 24 

Decimal Equivalents 269 

Diameters of Circles 273 — 277 

Land Measure 272 

Metric Equivalents 270 

Pipe, Standard Sizes of .Welded 279 

Roman Figures 272 

Solid Measure 272 

Wire Gauges 278 

Useful for Draughtsmen 266 — 280 

Tangent of an Arc, def 99 

To Draw a, to a Circle 91 

Tee-Iron, illus 75 

Tee-Square, Adjustable, desc. and illus 113 

Desc 112 

How to Use, illus in, 147 

Ulus 102, 112 



anical Drawing. 297 

PAGE 

Tee-Sqiiare, Points about 242 

Teeth in Bevel Gears, desc 204 

Terms and Definitions, Preliminary 41 

Test-Pieces, Use of, in Blue Prints 788 

Tetrahedron, def 48 

Theorem, def 83 

Thumb-Tacii illus 109, desc. no 

Tints and Colors, desc 184 

Title and Date, on Sketches 142 

Title, Date, Scale, etc.. Office Rules for 192 

Title Page vii 

Tracing-Cloth, desc 186 

Tracings, Office Rules for Keeping 195 

Tinted and Shaded, desc 184 

Trammels, desc. and illus 125 

Trapezium, def 48 

Trapezoid, del 48 

Trestles, Drawing-Board, desc. and illus no 

Triangle, def 50 

To Describe a Circle about a 93 

Triangle, or Set-Square, desc. and illus 114 



298 



Hawkins' Mechanical Drawing. 



Triangle, or Set-Square, How to Use. .desc. 147, illus. 166 

Triangles, illus 102 

To Construct 92 

Trigonometry, principles and def. 98 

Trisect, def 50 

Trnndle AVheel desc. 201, illus. 208 

Two-foot Rule, illus 128 

U. S. Standards, Pipes 279 

Upright Lines, How to Draw 61 

Useful Tables for Draughtsmen 269 — 280 

Valve, Blow-off desc. 174, illus. 175 

Valve Gear, or Link Motion, illus 225 

Vanishing Point, def. and illus 251 

In Drawing, illus 250 

In Perspective Drawing 252 

Varnish, Shellac, for Drawings 241 

Versed Sine of an Arc 99 

Vertex, def 51 



Vertex, Oi an Angle, def. 42 

Vertical, def • 51, 251 

Vertical liines, in Perspective 257 

Vertical-Plane, def 249 

View, def 51 

Visual Ray in Perspective Drawing 256 

Visual Rays of Light desc. 252, illus. 255 

Vulcanite, Section-Lining, illus 182 

Water Reflection in Perspective Drawing iUus 246 

WTieel, Bevel, A, illus 203 

Crown, illus 208 

Helical, A, illus 207 

Hub, Section-Lining, illus 184 

Internal Gear, desc •. 201, 207 

Miter, A, illus 204 

Proportions of the Teeth of a 210 

Spur illus. 198, desc. 199, 201 

Worm, desc 201 

IVood, Section-Lining, illus 182 

IVorking Drawing, Bending Machine aao-i 



Hawkins' Mechanical Drawing. 



299 



PAGB 

Working Drawing, Def 5i 

nius 218, 220, 221, 222, 223, 224, 225, 226, 228 

Bumping Post, illus 226 

Points, etc *4} 

Power Pnnching Press • • 222 

Numbering a, OflBce Rules for I95 

To Read a 229 



IVorking Drawings, desc 219, 227 

l¥orm-Gear, desc ^°^ 

Worm-^^Tieel desc. 201, iUns. 206 

Speed of a 

"Wrencb, illus 

"Wrist-Lines, illus 

Wroaght-Iron, Section-Lining, illus 



216 

75 

64 

182 



A GOOD BOOK IS A GOOD FRIEND 

To Our Readers : 

The good books, here described, de« 
serve more than a passing notice, consider- 
ing that the brief description under each 
title indicates only their wide scope, and is 
merely suggestive of the mine of useful infor- 
mation contained in each of the volumes. 

Written so they can be easily under- 
stood, and covering the fundamental prin- 
ciples of engineering, presenting the latest 
developments and the accepted practice, giv- 
ing a working knowledge of practical things, 
with reliable and helpful information for 
ready reference. 

These books are self-educators, and "he 
who runs may read" and improve his pres- 
ent knowledge in the wide field of modem 
engineering practice. 

Sincerely, 

Theo. Audel &- Co. 

Publishers 
72 5th Ave., N. Y. 



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for the practical engineer, covering as it does a 
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rine engines, boilers, pumps, and all auxiliary 
apparatus, the accepted rules for figuring 
the safety-valve. More than looo ready 
references, 807 Questions on practical ma- 
rine engineering are fully answered and 
explained, thus forming a ready guide in solv- 
ing the difficulties and problems which so often 
arise in this profession. 



if: $2 



AUDELS CONCISE 
DRAWING COURSE 



$1 



A SUMMARY of the matter contained in the work 
■^ will give a comprehensive idea of its value and 
^isefulness. 

1 Drawing Tools and Their 
Use 

2 Drafting Room and Shop 
Pr&ctic0 

3 Laying Out Sheets and 
Lettering 

4 Important Rules for Work* 
ing Drawings 

5 Three Views and Isometric 

6 Simple IVIodels 

7 Wooden Joints and Car* 
penter Work 

8 Machine Drawing 

9 Projections 

10 Sections 

11 Intersections 

12 Warped Surfaces 

13 Method of Plan of Eleva* 
tion 

14 Method of Vanishing Point 

15 Shades and Shadows 

16 Points, Lines and Planes 

17 Prisms and Pyramids 

18 Spheres 

19 Screw Surfaces 

20 Shadow Perspective 

Lessons in Advanced Practice, Working Drawings 

of a Globe Valve, Steam Engine and Electric Generator, 

Lessons in Elementary Designing and Construction, 

Riveted Joints and Structural Work, Cams, Tooth Gearing, 
Valve Motions. 

Fifty Plates of practical work with dimensions fo» 
practice, making it a complete text book on the subject 
for School Classes in the various branches of applied 
mechanics. 

The explanations in this book are simple and direct, 
stripped of all needless words, teaching the student to 
develop his own thinking power, and forms the basis 
of the course covered by the classes in Mechanical 
Drawing at Cooper Union Institute. There are 120 
pages, six subject divisions; 50 plates, size 6x9, printed 
on fine paper with red cloth cover. Price $1 postpaid. 




Hawkins* Electricity for Engineers. 

The introduction of electrical machinery in 
almost every power plant has created a great 
demand for competent engineers and others 
having a knowledge of electricity and capable of 
operating or supervising the running of electrical 
machinery. To such persons this pocket-book 
■will be found a great benefactor, since it con- 
tains just the information required, clearly ex- 
plained in a practical manner. 

It contains 550 pages with 300 illustrations 
of electrical appliances, and is bound in heavy 
red leather, size 4^x6^ for the pocket. 

Hawkins* Engineers* Examinations . 

This work is an important aid to engineers 
of all grades, and is undoubtedly the most help- 
ful ever issued relating to a safe and sure 
preparation for examination. It presents in a 
question and answer form the most approved 
practice in the care and management of Steam 
Boilers, Engines, Pumps, Electrical and Refriger- 
ating Machines, together with much operative 
information useful to the student. 

Hawkins* Steam Engine Catechism. 

This work is gotten up to fill a long-felt need 
for a practical book. It gives directions and 
detailed descriptions for running the various 
types of steam engines in use. 

The book also treats generously upon Ma- 
rine, Locomotive and Gas Engines, and will be 
found valuable to all users of these motive 
powers. 

Hawkins* Steam Boiler Practice. 

This instructive book on Boiler Room 
Practice is indispensable to Firemen, Engineers 
and all others wishing to perfect themselves ia 
this important branch of Steam Engineering. 

Besides a full descriptive treatise on Station- 
ary, Marine and Locomotive boilers, it contains 
sixty management cautions, all necessary rules 
and specifications for boilers, including riveting, 
bracing, finding pressure, strain on bolts, etc., 
thus being a complete band-book on the sub- 
ject. 



$2 



$2 



$2 



$2 



Hawkins* Mechanical Drawing. 

This work is arranged according to the cor- 
rect principles of the art of drawing; each 
theme being clearly illustrated to aid the student 
to ready and rapid comprehension. 

It contains 320 pages with over 300 illustra- 
tions, including useful diagrams and suggestions 
in drawings for practice. Handsomely bound 
in dark green cloth. Size 7x10 inches. 

Hawkins' Calculations for Engineers. 

The Hand Book of Calculations is a work of 
instruction and reference relating to the steam 
engine, steam boiler, etc., and has been said to 
contain every calculation, rule and table neces- 
sary for the Engineer, Fireman and Steam 
User. 

It is a complete course in Mathematics. All 
calculations are in plain arithmetical figures, so 
that they can be understood at a glance. 



Hawkins* Steam Engine Indicator. 

This work is designed for the use of erecting 
and operating engineers, superintendents and 
students of steam engineering, relating, as it 
does, to the economical use of steam. 

The work is profusely illustrated with working 
cards taken from every day use, and gives many 
plain and valuable lessons derived from the 
diagrams. 

Guarsmtee. 



$2 



$2 



$1 



These books we guarantee to be in every 
•way as represented, and if not found 
satisfactory can be returned promptly and 
the amount paidwill be willingly refunded. 
All books shipped post paid. 

Remittances are best sent by Check, 
Post Office or Express Money Orders, 



